AV I MR.BARNARD PIERCE MRS.SCCARL HAESSLERR HO. 11WARD LuJCE MISMRAE KIH CORRECT CONTRACT BRIDGE CORRECT CONTRACT BRIDGE BY E. V. SHEPARD President, Shepard's Studio, Inc., author of Scientific Auction Bridge, Correct Auction, Etc. Including the official laws of Contract Bridge adopted by The Whist Club, New York, and by all of the leading Clubs in America. GARDEN CITY DOUBLEDAY,:::: NEW YORK DORAN & COMPANY, INC. 1929 COPYRIGHT, 1929, BY E. V. SHEPARD. COPYRIGHT, 1927, BY THE WHIST CLUB, NEW YORK. ALL RIGHTS RESERVED. PRINTED IN THE UNITED STATES AT THE COUNTRY LIFE PRESS, GARDEN CITY, N. Y. -CFIRST EDITION CONTENTS CHAPTER PAGE I VIVE LE Roi........ 3 Brief History of Contract Bridge. II SYNOPSIS OF THE LAWS OF CONTRACT BRIDGE.......... 4 III COMMENTS......... 7 Comparison of Contract with Auction Bridge. IV BASIC PRINCIPLES....... 10 Average Strength-Sure Tricks-Declarer's and Dummy's Honor Values - Rectifying Values - Trump Values - Valuing Dummy's Trumps - Accurate Valuations Are Vital. V OPENING BIDS........ 23 Dealer's or Second Hand's Suit Bids-Compensated Bids - Dealer's or Second Hand's NoTrump Bids-Practical Contracting-Choosing Between Trumps and No-Trump Bids - TwoSuiters-Preemptive Bids. VI OPENING BIDS........ 37 Third or Fourth Hand- Late Minor Bids - Minor Suit Conventions. VII OPENING TWO-BIDS...... 4I Two-No Trump-Second Use of Two BidsThe Reverse Signal-Trump Strength and Side Weakness. VIII FORCED BIDS........ 48 Improving Partner's Bid - Partner's Probable Assistance - Forced No-Trump Bids - Bidding Against No-Trumps - Contract and Auction Strategy Differ-Bidding Against No-Trump at Right. CHAPTER PAGE IX INFORMATORY DOUBLES..... 66 Basic Facts to Consider-Doubling Slamr Signals -Rules for Informatory Doubles-Subsequent Doubles-Repeating a Double-Doubling Each of Two Suits-Assisting Doubles. X RESPONSES TO INFORMATORY DOUBLES..... 87 General Principles Governing Doubles - Responses to No-Trump Doubles —The Business Pass-Responses to Subsequent Doubles-Voluntary Responses. XI OVERCALLING DOUBLES..... 99 Redoubling-The Informatory Pass. XII ASSISTING PARTNER..... I04 Rule of Five-Contracting Strategy-Rectifying Dummy's Trump Values. XIII REBIDDING......... I II Unassisted Rebids. XIV BUSINESS DOUBLES...... I17 Overcalling Partner's Double-Relative Values of Games and Penalties-Overbidding to Save Slams-Sure Tricks Shown'by Partner's Bids. XV GOULASHES...126 Comments on Goulash Laws-Goulash Bidding -The Double Take-Out. THE INTERLUDE..... I34 XVI AVERAGES AND PROBABILITIES.. 135 Card Distributions. XVII LAWS OF SYMMETRY.. 38 Glossary of Symmetry-Limits of SymmetryPractical Results. CHAPTER PAGE XVIII UNNECESSARILY'HIGH BIDS.. 143 Preemptive Bid —Game Signal-Slam SignalDemand Bids-Obliging Bids-Forcing Bids. XIX FOUR-CARD BIDS....... 145 Inherent Weakness of 4-Card Suits-Five-Card Suits Most Frequent. XX CONTRACTING POWERFUL HANDS.. 50 Topography of Contract-The Short Suit System - The No-Trump System-Comparison of Systems-Analysis of Opening Two-Bids. XXI THE CLUB CONVENTION.... 164 SLAM BIDDING...........167 XXII SLAM BIDDING SIGNALS......68 Slam Signals-The Stop Signal-The Reverse Signal-Showing Aces —Showing Kings and Queens-Bidding Opponent's Suit-Showing a Two-Suiter-Showing a Suit. XXIII THE FIT OF HANDS... I80 Safety First-Showing All Side Aces-Bidding No-Trump Slams. PUZZLING HANDS....... g90 XXIV DETERMINING PROBABLE RESULTS. 191 The Point System-Partner's Probable Strength -The Rule of Three-Probable Game Chances Wihen an Opponent Has Bid. XXV THE Two-No TRUMP APPROACH. 201 Taking Out 2-No Trumps. THE LAWS OF CONTRACT BRIDGE. 215 CORRECT CONTRACT BRIDGE I VIVE LE ROI E roi est mort, vive le roil Auction Bridge has L passed on. Club and Society hail the accession to rule of Contract Bridge. Americans were not ready for Contract when it sought recognition fifteen years ago. I think that my pupils in 1924 were the first to really study the game and that my book on Contract, published January i i, 1927, was the first one printed in the United States. On January 25, 1927, the Knickerbocker Whist Club issued the first official Laws of Contract Bridge. September 15, 1927, the present "Laws of Contract Bridge" were issued by the Whist Club, with the approval of the leading card clubs and organizations of the country. Contract, better than Auction, expresses the spirit of the times-speed, thrill, verve. The old guard fought hard for Auction, just as those of a past generation defended Whist, but in both cases progress demand the change. As yet a mere handful of players have sensed the vital differences between the newer and older games-the vast majority of players, including former Auction authorities and experts, merely changed their scoring, bid higher, called their altered procedure Contract, and continue to play Auction. In reality Contract strategy and technique are unique, and necessary to obtain maximum scores with minimum risks. 3 II SYNOPSIS OF THE LAWS OF CONTRACT BRIDGE THROUGH THE COURTESY OF THE WHIST CLUB, NEW YORK TRICK VALUES No Trumps 35; Spades 30; Hearts 30; Diamonds 20; Clubs 20; Doubling doubles trick values. Redoubling multiplies them by four. G A M E A game is won when one side makes a contract score of o00 or more points. Of the tricks made, only those contracted for are scored in the contract score. All tricks made over and above those contracted for are scored in the honor score. RUBBER A rubber is ended when one side wins two games. VULNERABLE After a side wins one game they become "Vulnerable." Until a side wins a game, they are "Not Vulnerable." PREMIUMS All premiums are scored in the honor score and are classified as follows: 4 LAWS OF CONTRACT BRIDGE 5 Honors: Points 4 in one hand....................... 10oo 5 in one hand....................... I50 4 aces in one hand in No Trumps........ I50 All other..................... None For Winning Final Game of Rubber: Points If a two-game rubber................. 700 If a three-game rubber............... 500 Making Contract: If Undoubled................. None If Doubled (When Declarer is Not Vulnerable)............... 50 (When Declarer is Vulnerable) Ioo Extra Tricks: If Undoubled (When Dealer is Vulnerable or Not Vulnerable), per trick 50 If Doubled (When Decldrer is Not Vulnerable), per trick....... I00 (When Declarer is Vulnerable), per trick.......... 200 Slams Bid and Made: Little Slam (When Declarer is Not Vulnerable).............. 500 (When Declarer is Vulnerable) 750 Grand Slam (When Declarer is Not Vulnerable)............... oo000 (When Declarer is Vulnerable..50................01 Unbid Slams Made..................... None Slam premiums are additional to all other premiums. Doubling and redoubling do not alter slam premiums. 6 CORRECT CONTRACT BRIDGE P E N A L T I E S Undertricks (Scored in Adversaries' honor score): If Undoubled (When Declarer is Not Vulnerable), per trick..... 50 If Undouirbled (When Declarer is Vulnerable) for first trick............ o100 for subsequent tricks, per trick................ 200 If Doubled (When Declarer is Not Vulnerable) first two tricks, per trick. ioo for third and fourth tricks, per trick.......... 200 for subsequent tricks, per trick............... 400 If Doubled (When Declarer is Vulnerable) for the first trick....... 200 for subsequent tricks, per trick.............. 400 Redoubling doubles the doubled premiums and penalties except those for slams. REVOKE The revoke penalty for either side is the loss of two tricks for any player's first revoke. One hundred points additional penalty for each subsequent revoke by the same player. III COMMENTS CONTRASTED with Contract, Auction is flabby, plodding, and primitive. Contract is the most perfect he-man's and she-woman's game ever devised-strenuous enough to tax to the limit the reasoning and courage of the former, sufficiently subtle to call forth all the intuition, imagination, and wiles of the latter. Three no-trumps, four of a major suit, or five of a minor suit must be bid to score game at a love score. If you bid one and win seven-odd, only the one trick bid counts towards game, the six overtricks must be scored at 50 points each in your honor column-a poor substitute for scoring both game and a huge premium for a grand slam contract fulfilled. In case one or two tricks will give you game it is unwise to bid higher, unless slam is clearly shouted by your cards, as the 50 points bonus for overtricks will exceed the trick value of a higher contract. Unless you can safely outbid opponents and score game or slam, or unless you can surely collect a penalty for an opposing rebid, it is not sound strategy to overcall a final declaration of an adversary that is below game value. Many a game is lost by affording an opponent another opportunity to bid. Three rubbers an hour, at 400 points per rubber, 7 8 CORRECT CONTRACT BRIDGE is the average at Auction. You will average only two rubbers of Contract an hour, at io0o points each. For a given period of time Contract at half Auction stakes will give about the same final settlement. Contrary to the commonly held opinion of the inexperienced, Contract is less of a gamble than Auction, as luck plays a lesser role in the newer game. Expert bid and play are of nearly equal importance. It calls for great ability to properly contract many hands and it requires unusual skill to squeeze the last possible trick from opponents, whether to win the last trick needed to fulfill a doubtful contract, or to take that one trick required to defeat an opposing make. The low pressure Auction cannot develop such skilled bidders and players as the high pressure Contract that never permits a player to go out of training. Rule-of-thumb valuations, unsound declarations, weak rescues, and poker tactics are vastly more dangerous than at Auction. Errors in judgment or strategy often cost ten times what they would at Auction. Why has Auction not been standardized after thirty years of play? There are two contributing causes: Whist traditions that failed to hold good at the newer game and because each "authority" has fought for pet theories that were not wholly sound. Auction teachings must be debunked before attempting to apply them at Contract. I know that it took me five years' investigation to discover what COMMENTS 9 Auction procedure was a part of sound Contract. Without such labor or unless he receives proper instruction, no Auction player can become a Contract expert. The best players will chiefly consist of those who never knew Auction and had nothing to unlearn. IV BASIC PRINCIPLES CONTRACT Bridge is a business. Your capital is the tricks that can be won. You and your partner exchange by means of declarations information concerning the number of tricks that each can win, to determine just what your joint resources justify undertaking. A pass says: "Partner, I hold nothing above average strength." Therefore just what constitutes average strength is the starting point of expert contracting. The following is a typical example of an average hand Io 7 A J 9 5 3 K 8 4 Q62 That the above hand contains just one card of each denomination is unimportant, so also are the suit lengths held. The important facts are the values held. These are 5 probable tricks if played with the longest suit as trumps; 334tricks' aid for partner at no-trumps; I 4 probable defensive tricks against a trump declaration in the poorest suit held. Each one of these three features is just average strength, hence the whole hand is average, and does not justify an opening bid. SURE TRICKS The foundations of important structures should rest on bed rock. The chief weakness of nearly all players' games is a partially unsound foundation, IO BASIC PRINCI-PLES I I liable at any time to result in serious losses. The first requirement for a sound opening hid is at least two sure tricks-the equivalent of two aces. X sure trick is a dependable one, whether or not - your side names the final declaration, and whether the contract is at trumps or no-trumps. As either declarer or dummy can ordinarily trump the third round of a suit you usually must win your defensive tricks on either the first or second round of a suit. The A K Q J of a side suit (one not the trump) has a probable defensive value of only two tricks, because its third round probably will be ruffed. Tables of "Quick Tricks" give many values that are not sure tricks, because they fail to allow for the probable ruff on the third lead of a suit. Early in I926 I abandoned the use of quick trick values, considering them obsolete, substituting for them something more modern, reliable, and simple. For practical purposes, only these five sure trick values need be memorized: A K, 2 tricks; A Q, i Y2 tricks; A, i trick; K Q, i trick; K X, Y2 trick. An A Q ibs given its i 2 defensive tricks because it ordinarily can win 2 tricks in case the missing K lies at its right and only a single trick if the king lies back (at the left) of the A Q. As equal chances exist for the K to lie in either of those two positions the average value of the A Q must be i 2 tricks. In like manner the average value of the guarded king (K X) is /2 defensive trick, because the ace is equally liable to lie at the right or at the left, half the time being able to capture the king and half the 12 CORRECT CONTRACT BRIDGE time allowing the king to win a defensive trick. When held in suits of fewer than four cards it is true that sometimes /4 trick values may be assigned to J's and Io's. But for purposes of opening the bidding you need not bother wfth [such "chicken feed"; unless you can count two full sure tricks in the five honor combinations already given, your hand is too weak for an opening bid. Sure tricks are the "commanding honors" that win defensive tricks against trump declarations, that stop the run of opposing suits at no-trumps, that enable your side to gain entry and utilize your resources to the best advantage. Sure tricks are very important factors, but 2 sure tricks exceed average by only 4 trick, so that some added reason is required for opening the bidding. This reason may be found either in a suit sufficiently long to rebid, or because you hold at least 4 assisting tricks for any declaration made by your partner. As ordinarily the declaring side controls trumps, honors held by the declarer or dummy possess greater value than those fit only for defense. DECLARER'S AND DUMMY'S HONOR VALUES In the long run it makes no difference whether honors are held by declarer or dummy, their values are the same, whether at a suit make or at no-trump. Only the five following values need be memorized: A X, I12 tricks; K X, I trick; Q X X, 4 trick; JX X X, Y2 trick; io X X X, 4 trick. BASIC PRINCIPLES '3 13 To be worth its full value, an honor heading a suit must be accompanied by at least as many smaller cards of its suit as there are X's given above (A or K, at least one guard; Q at least two smaller cards; J or IO must have at least three smaller cards). For each small card that you take away from the required number of guards you deduct 3/4 trick from the value of the honor (K singleton only counts as /4 trick; Q X is worth only 3/2 trick; the Q alone counts 34 trick; etc.). Unless a suit is the trump, additional guards add no value to an honor. When the higher of two honors of the same suit is sufficiently guarded, the lower honor attains full value in case it is followed by a single lower card (K io X, for example; as the K is fully guarded the IO needs only the smaller card to give the IO its value of 34 trick; the combined honors have the sum of the individual values of the two honors, or i 4 tricks. The J io X counts only Y2 trick, because the J loses 34 trick by being accompanied by only two instead of three lesser cards). Ordinarily, natural laws are very simple; remembering that the thrice guarded IO is worth 34 trick, you obtain the value of the next higher honor (the J) by adding 34 trick; the Q is another 34 trick more valuable; the K counts four 34th tricks, being the fourth honor, or one full trick in value. The value of the A jumps to i 2 tricks, due to the fact that it is the only single honor having full active value. Other single honors possess passive value, because you must have some other player lead their I4 CORRECT CONTRACT BRIDGE suit, whereas an ace can be led and still be certain of winning a trick. How can an ace win i 12 tricks? It cannot do that, but half the time that you hold an ace its presence will add a full trick to the value of partner's cards, by enabling him to win one trick that could not be taken if an opponent held your ace. The direct trick taking value of the ace is one trick, its promotional value is an added Y2 trick, making the total worth of the ace I 2 tricks. All this has been proven, by actually placing in rotation the other four honors in each of the 8i different positions that they can occupy in the hands of the three remaining players; tabulating the total number of tricks won in the 81 'hands, then listing the number of these tricks that could not be won unless you held the guarded ace, and so on with each other honor or honors possible for you to hold. While the laborious process consumed several weeks' time, it resulted in obtaining real values, instead of the rougher approximations previously in use. The process also proved that for the purposes of declarer or dummy such honors as K Q X of a suit are worth the same as the K X of one suit and the Q X X of another suit. Keep clearly in mind the distinction between sure trick values, which are wholly defensive values against trump declarations, and honor values which only hold good when you are declarer or dummy. The ace has a defensive value of only one trick but its value to declarer or dummy is I 2 tricks. The Q X X has a defensive value of only 4 trick but its BASIC PRINCIPLES I5 honor value is Y4 trick. The Q X X X has no defensive value but its honor value to either declarer or dummy remains 4 trick. Few players can mentally multiply fractional values and many find it difficult to even add together several fractions. The easiest way for most players to value hands is to select two fractions which jointly equal an even number of tricks. For example, the holder of the following no-trump hand might proceed as follows: * A IO4 2 K Q 3 * A85 0 AKJ6 A A plus * A, 3 tricks; 4 io and ' Q, 4 tricks (total to date); Q K and 0 K, 6 tricks; 0 A J, 8 tricks. A few players prefer to count honors just as they come, thus: i/2, 14, 2Y4, 3Y2, 5 62, 72, 8 tricks total. Of course a player will naturally count his values in the way coming easiest to him. RECTIFYING VALUES An adverse suit bid necessitates a revaluation of honors held -in opponent's suit. In the first place such honors can possess no probable promotional value, because your partner is not likely to hold honors also. Honors of opponent's suit possess only positional value. For example: your K J 6 of opponent's suit should be worth 2 (instead of their ordinary value of i y2) tricks, if held back of their bidder; your honors have no probable value if held at his right, as he almost certainly can lead through your strength and pick them up. i6 CORRECT CONTRACT BRIDGE TRUMP VALUES Honor values are identical for both trump and unbid side suits, whether held by declarer or dummy. Low trumps held by declarer and dummy slightly vary in values, because they possess different advantages. Of course values can be calculated to any desired degree of accuracy, but for practical purposes I have found the following sufficiently close. Four, five, or six card suits, when headed by A K Q J, are called "thoroughly established," and may be valued at a trick per trump. Suits of 7 or 8 cards require only the A K Q to be valued as "thoroughly established." The high trumps needed to capture opposing cards are termed "essential honors;" the smaller trumps remaining after opposing trumps have been pulled are called "long trumps." Unless thoroughly established, declarer's trumps average to be worth the sum total of the value of individual honors held, plus 4 trick for the fourth trump, plus one full trick for each trump held beginning with the fifth. AVERAGE VALUE OF 4 TRUMPS A K Q J 4 tricks A Q X X 2~ tricks A K Q IO 34 " A J IOX 22 A K J IO 32 " A J X X 24 A K Q X 3Y2 " A ToXX2 2 A K J X 3~ 4 AXXX iY4 AKIoX3 " K Q J X 2 A K XX 2 /4 K Q 10 X 24 A Q J TO 3 4 K J IO X 2 A Q J X 3 " KQXX 2 A Q IOX 24 K J XX iY4 BASIC PRINCIPLES 17 K Io X X i2 tricks Q XX X I trickt K X XX I4% " J IO X I QJ IoX I4 JXXX X " Q J X X I2 o X X X X Y Q Io X X 4 " XXXX y4 To obtain the values of longer trump suits add one full trick for each trump held in excess of four. VALUING DUMMY S TRUMPS Dummy's honors possess the same value as though they were held by the declarer. Dummy's trumps lower than the 10 possess special values differing from those of the declarer. Three low trumps are termed "normal support," on the assumption that the declarer holds just five trumps, leaving only five trumps to be divided between the two adverse hands, so that three leads of trumps probably will drop all opposing trumps. More than three trumps in dummy quicken the process of pulling opposing trumps. On this account dummy may value 4 trumps at Y2 trick, and dummy may count 5 or more trumps as worth one full assisting trick. These values added to dummy because more than the normal 3 trumps are held, are in addition to any values due to trump honors held or values due to ability to trump short side suits. Dummy must deduct from the outside values held in the hand /2 trick for each trump by which he falls short of 3 trumps (2 trick for 2 trumps; I trick in case only a single trump is held; i 2 tricks for being void of trumps). The declarer cannot count anything because he is i8 CORRECT CONTRACT BRIDGE short of a side suit. (He cannot count his trump tricks more than once; if he utilizes trumps for ruffing opponents' suits the declarer wins no more tricks than he would if he led an extra round or two of trumps, instead of employing those trumps for ruffing). It is different with dummy's small trumps, as they cannot win tricks unless they can be utilized to trump suits whereof dummy happens to be short. Count dummy's probable trump tricks for ruffing as follows: Trumps Held Void Suit Singleton Doubleton 3 or more 2 tricks I trick 2 trick 2 I " O I 0 "0 0 " ACCURATE VALUATIONS ARE VITAL Nobody wants an inaccurate cashier or a partner who cannot count tricks. Able players sometimes deny that they count tricks; perhaps long experience enables them to unconsciously value hands, but consciously or otherwise, every winning player must be able to quickly and accurately value the hands he holds. Whenever you have occasion to study either a published hand or one spread on the table, painstakingly count your tricks as given in this chapter; continue this process until you also can tell at a glance your defensive, assisting, and declaring strength. The following hands illustrate the mental process to employ in trick counting. BASIC PRINCIPLES I9 In diagrams of hands Z is always the dealer, who must first bid or pass. The first thing to do is to count defensive tricks (call them what you likedefensive tricks, sure tricks, commanding honors, or quick tricks, provided in the latter case that you employ only values attaching to the A K, A Q, A, K Q, and the guarded K, omitting other honors as useless to Contract needs). 4 IO 82 v 9873 * AJ 0 IO 7 6 5 A Q 9 7 4 4 KJ 5 v AJ Io A B Q 5 4 * 9 4 4 Io 6 5 3 0 Kg8 Z 0 AQ3 4 63 V K 6 2 * KQ872 0 J42 Taking them in regular bidding rotation the players hold the following "sure tricks" (those having probable defensive values against trump makes): Z: in hearts Y2 trick, with I full trick in clubs; total i Y2 sure tricks; A has i Y2 spade tricks; i heart trick (if it were worth while we would give him the more exact value of i Y heart tricks); y2 diamond trick; total for A, 3 tricks against an opposing trump declaration. Y holds in clubs just i full defensive trick, the sole probable defensive 20 CORRECT CONTRACT BRIDGE strength of the entire hand. B has 2 trick in spades and I y defensive diamond tricks, a total of 2 sure tricks (a very precise man would add to the value of the hand 54 trick for hearts, which is too vague a value for Contract needs). The total defensive values of the four hands are 7X2 tricks (or 8 tricks, if you choose to split hairs). A hand may give the four players as high as 10 defensive tricks or as low as 5 tricks, the average being about 754 "sure tricks." You may readily verify this last statement by dealing a few hands and counting the defensive tricks. Lacking the two sure tricks needed to open the bidding, Z need not even bother at first to note the value of his best make as declarer, or his aid for a possible declaration by his partner. A having a trifle better than 3 sure tricks must at once value his cards for declaring purposes. At spades his hand counts 3 2 probable tricks in trumps; 2 heart tricks; nothing in clubs; I diamond trick; total 6X2 tricks, provided spades happens to be the best make for the joint holdings of A and B. Y's hand is too weak to require valuation. When A opens the contracting with I-Spade, B must count his assisting values for that make; B's cards are valued as follows: spades, i /2 tricks; hearts, Y4 trick; clubs, 4 trick; diamonds, 2%4 tricks; total 454 tricks. It is important to count even the least fractions of tricks as declarer or dummy, as the sum total of fractions may equal several tricks. The total trick counting for A-B yields a final value of i 4 tricks for the two hands, and they can win just 5-odd, as the cards BASIC PRINCIPLES 21 lie. Y and Z can win only 2 of the 2~ defensive tricks jointly held. Try checking up the defensive, declaring and assisting tricks on the following.hand. K Q o 8 5 v 972 * 93 0 AK5 4 J76 Y 43 v K6543 A B v AJ8 4 52 * 10 876 0 J 76 Z 0 Q942 A92 Q io * AKQJ4 0 Io 8 3 Sure tricks count as follows: Z, 3; A, Y2; Y, 3; B, i; total 7Y2. With spades as trumps Y's declaring strength is: spades, 3%; diamonds, 2/2; total declaring strength, 5 4 tricks. Z's assisting strength is: spades, i % tricks; hearts, Y4 trick; clubs, 4 tricks; total 654 tricks. The probable joint strength of the hands is just I2 -tricks. Against a normal opening lead of B's lowest diamond Y would make a little slam, but in case Y bid a little slam at Contract, B would lay down his top heart and another lead of hearts would hold Y down to 5-odd. Trick counting that extends beyond 10 is unreliable, often depending for realization upon a favorable opening lead. The next hand shown was played at no-trumps, 22 CORRECT CONTRACT BRIDGE making 4-odd. The hand of the declarer (Z) counts 4X2 probable tricks, while that of dummy (Y) counts 6 tricks; a total joint value of io02 probable tricks at no-trumps. * K3 V A82 * QJ6 0 KQJ84 Y I Io 7 4 2 v J IO 3 4 95 0o O 6 5 2 J86 V Q765 4A 8 4 2 0A9 AQ95 v2 K94 4 K Io 7 3 0 73 V OPENING BIDS MASTERY of Chapter IV is the first step towards expert contracting. Players clinging to Auction methods of valuation and bidding will gravitate to the bottom of the class. Only live wires head Contract classes. Ninety per cent of all dealt hands need at least two contracting rounds to determine partners' best procedure. Never hastily cry "Eureka I" First make certain that your side's best program has been discovered. To 'be understandable, partnership contracting must be somewhat conventional; each declaration requires fulfillment of definite minimum requirements. A pass betokens nothing obligating an immediate declaration; it does not deny possession of strong holdings worth high secondary bidding. The hand shown below must not be utilized for an opening bid, because it lacks even a single commanding honor but as high as 4-Spades may be bid later. No danger exists that someone will not hold cards worth an opening bid. * QIo98765432 V 7 4 63 3 Adversaries may win as many as six tricks or the hand may win as high as nine tricks; its probable value is eight tricks. A primary pass and secondary 23 24 CORRECT CONTRACT BRIDGE bidding up to 4-odd gives partner the best possible picture of the holding. Because partner must furnish at least one trick to enable game to be won, he must not be deceived by utilizing the hand for an opening bid. A hand requiring no aid from partner to go game, if lacking slam probabilities, is above all rules. I recently held the hand depicted below and opened with 4-Spades, because I could count ten certain tricks and because my partner's chances of holding at least two of the three honors missing from my two-suiter were less than i in 4, rendering a little slam too visionary to consider. Neither A nor B dared risk a declaration of the 5-Hearts that they could make, but had I passed or bid less than 4-Spades they would have gone game or I would have been obliged to save game by an overbid of my values held. 4 764 4 A9765 0 5432 4 A7 Y & K6 AQ 92 A B 2 K J 8 5 3 4 K J 8 3 * Q I 4 2 0 87 Z 0 A6 Q J io 9 8 5 3 2 ---- 0 K Q J 0o 9 OPENING BIDS 25 A "business bid" is one made needlessly high to show game or slam expectations. The preemptive 4-Spades used above leaves no question in partner's mind. "Informatory bids" are those made no higher than required by circumstances; they announce fulfillment of standard requirements, leaving partner free.to utilize the information given in such ways as his hand justifies. If sound, an "approach bid" is synonymous with an "informatory bid," but many players apply the term approach bid to an unsound declaration belonging to "poker tactics"very much out of place in Contract though common enough at Auction. DEALER'S OR SECOND HAND'S SUIT BIDS By common consent or because of scientific reasons there are definite minimum requirements for opening the contracting. Either dealer or second hand must meet each of the following requirements, to open the bidding: I. Hold two sure tricks; 2. Have one sure trick in trumps (unless a "compensated bid" can be made); 3. Have four trumps; 4. Have three probable trump tricks; 5. Have probable ability to win four tricks total. Unless worth a rebid the hand must be worth four assisting tricks if partner prefers no-trump. i Club 8 3 2 Iv KJ7 4 AQJ6 0974 i Spade A K9 6 3 v 85 4 954 0 A86 26 CORRECT CONTRACT BRIDGE The above two hands merit the indicated opening bids, as they fully meet each of the minimum requirements. Pass 4 74 v AQJ I05 4 I03 0 QIo62 Pass 4 53 VQJ62 4 865 ) AK974 The first of the above hands lacks its two defensive tricks needed to exceed a hand of average strength, and is not worth an opening bid. The second hand contains two defensive tricks, but it cannot properly be rebid nor does it have probable ability to aid partner by more than 2 Y4 tricks, whereas 4 assisting tricks are required. i Heart 4 8 5 4 I AKJ863 4 6 3 0 7 6 i Heart 4 6 v KQ7542 4 A97 0842 Both above hands fall short of ability to aid partner to even a normal amount; ability to rebid the hands is the sole excuse for making an opening bid. Sound informatory bids serve several useful purposes: they show the best defense against opposing makes and a well guarded suit in case partner wishes to shift to no-trumps; such bids either disclose at least 4 assisting tricks or ability to rebid; they also encourage partner to make certain that game-going hands shall not pass out. Third and fourth hands hesitate to open the bidding unless game appears probable or unless quite confident that opponents cannot make secondary declarations that will go game. Therefore it is the duty of the dealer and second hand 'to make sound opening bids and to avoid misleading ones. OPENING BIDS 27 COMPENSATED BIDS A "compensated bid" is a suit declaration of a hand containing such excess strength as to atone for lack of sure trick strength in the suit bid. If at least two sure tricks are held, provided the hand is worth not less than six tricks total, any suit of five or more cards worth three tricks as trumps may be utilized for an opening bid. i Spade 4K J Io 9 6 v 73 * O 85 0 AKQ iHeart 4 A5 v JIo8632 4AK O J73 Pass Q J Io 8 5 v io 6 * 97 4 0 AK6 There can be no question as to the soundness of opening the contracting on the first two hands given above. The third hand is barely average and fails to justify an opening bid; should another player open the bidding a forced bid of I-Spade is called for. D E A L E R 'S OR SECOND HAND 'S NO-TRUMP BIDS Probable no-trump tricks are also probable assisting tricks for partner. The minimum requirements for an opening no-trump bid by either dealer or second hand are: 1. Two sure tricks; 2. Three guarded suits with probable ability to - win five tricks, or four guarded suits with probable ability to win four tricks. Minimum guarded suits are A X, K X, Q J X, - 28 CORRECT CONTRACT BRIDGE Q Io X, Q X X X, J io X X, J 9 8 X, or any suit of five cards. I-NoTrump 6 QJ84 v A o8 4 732 0 AJ6 i-NoTrump A A 8 5 K 97 K 7 6 0 J9 8 3 Pass i A74 v A 65 * 963 0 K642 Pass 4 8532 v 743 * AKQ 0 A98 The first of above hands contains five probable tricks in three guarded suits; the second hand has four probable tricks in four guarded suits; either affords the minimum allowable bid. Neither of the last two hands affords any excuse for opening the bidding. PRACTICAL CONTRACTING As a surveyor gives precise lines beyond which an owner must not build, so rules for making opening bids give to a hair the limit for a player to go. Neither surveyor nor rule advises venturing the possible limit without a sound reason. The minimum requirements given may habitually be employed at the less exacting game of Auction, but the bidding mechanism of Contract is more complex, requiring a special reason why a bidder should open the contracting on fulfillment of absolute minimum requirements. Auction custom has sanctioned opening bids barely meeting minimum requirements, because harm seldom results and because partner assumes a pass to indicate sub-normal cards. It is poor Contract strategy to open the bidding unless willing to rebid for game or slam in case partner carries the contracting to within one trick of OPENING BIDS 9 29 either; on which account it ordinarily is poor contracting strategy to open the bidding on weaker than a 5-trick hand, so that you can once rebid, if necessary. But one sound excuse exists for making an opening bid of a 44trick hand-because your partner is a timid bidder who will not venture to open contracting as third or fourth hand unless he holds overwhelming strength. You feel obliged to encourage such a partner to declare and you also feel certain that he will never raise your declarations to the limit of his strength. Under such conditions you will be justified in rebidding your 4-trick hand in case partner carries you within a single trick of game. CHOOSING BETWEEN TRUMP AND NO-TRUMP BIDS At love score it takes 3 no-trumps, 4 at a major or 5 at a minor suit to go game. Honors have equal trick values at no-trump and at a suit make. A 4-card suit averages to be worth only Y4 trick more at trumps than at no-trump, but longer suits (unless thoroughly established) may be valued at one full trick for each card more than four if played at trumps, whereas at no-trump it may be impossible to establish the long cards of a suit before opponents have saved game. In general, major suits of five or more cards had best be played at trumps, unless all four aces are held, so that game appears certain at either make and the honor count of iSo 30 CORRECT CONTRACT BRIDGE points is desired at no-trump. If slam possibilities are apparent the four aces may be disregarded, as slams are easier at trumps than at no-trump. Four-odd averages to be scored four times as frequently as 5-odd. On this account four guarded suits make no-trump preferable to a minor trump make. Disregard pseudo-scientific statements concerning "hand patterns" (The way your 13 cards are divided between suits); safe deductions as to what others hold, judged from your own type of hand, are extremely limited in number and of uncertain value, as has been conclusively proven mathematically. When considering no-trump declarations the 4 4 3 2, 4 3 3 3, or even the 4 44 I pattern of your hand is less important than are certain other factors. Singletons are not the kobolds that some players believe. The fact is that your partner's chances to effectively stop a suit increase as your suit becomes shorter. No player likes singletons when he contemplates bidding no-trump or when he has only four trumps-there being little to choose between the two unpleasant situations. As partner is more prompt to shift a minor than a major declaration any sound opening minor bid is preferable to no-trump with one unguarded suit (9 7 4 2, 9 7 2,4 2, or 2, held make no difference), except in the rare case when nearly solid tops in three suits make it improbable that partner or opponent will be able to overcall a minor make, rendering it necessary to bid no-trump. OPENING BIDS 3I Ability to win at least three trump tricks should be labelled sine qua non when considering opening contracting with a suit declaration. This is not so imperative at minor makes as at major calls, because partner will more often raise to his limit a major suit declaration. The only 4-card suits averaging three trump tricks' value are: A K Q X, A K J X, A K io X, A Q J X, and K Q J io. With four guarded suits the major suit declaration has only a shade's preference over no-trump. With a single poorly guarded suit a sound 4-card suit bid is distinctly safer than no-trump. With major suits worth fewer than three trump tricks, if three suits are guarded, no-trump is a sounder declaration than trumps. It has been a custom of questionable character to bid i-No Trump or two short solid suits, if neither suit afforded a sound suit declaration (A K Q and A K Q, for example), although the remaining two suits are wholly unprotected; unless partner can bid it is improbable that game can be won at no-trump and it is reasonably certain that opponents cannot go game; on these accounts such notrumps with two hopelessly weak suits appear unwarranted. i Spade* AKJ6 v KQ73 495 O Qio6 i Club * 95 V KQ73 * AKJ6 O Qio6 i Heart * K 7 5 v A Q J 4 * K 9 7 O A83 iNoTrump*K75 7 K97 * AQJ4 O A63 I NoTrump * AQ64 AQ97 * A853 06 iDiamond*AQ84 V6 *A853 OAQ97 32 CORRECT CONTRACT BRIDGE TWO-SUITERS About I in 20 hands contains two suits having five or more cards in each, called a "two-suiter." Allowing partner a choice of two suits doubles his chances to strongly support the one selected as trumps. The requirements for dealer or second hand to open the bidding on a two-suiter are: I. Two sure tricks held in the hand; 2. Each suit bid worth three probable tricks as trumps. The fact that you offer partner a choice of suits justifies slightly shading the requirement of holding three probable trump tricks, as illustrated in the hands given below. The first hand justifies bidding both hearts and clubs. The second is a permissible i-Heart hand, rather than i-No Trump, but the third hand calls for I-No Trump instead of the secondary club declaration justified by the two-suiter make-up of the first hand. 4 A8 v A i 84 3 4 K I 7 5 2 0 4 A A8 <P A 8 4 3 * K I 7 5 0 42 A8 A Io 8 4 * K Io 7 5 2 0 42 Only in case partner has opened the bidding with no trump and has then bid 2-No Trumps over the display of your best suit are you justified in even considering showing an impotent second suit. It is then a close question whether the hand shown below should be bid 3-Hearts or 3-No Trumps, OPENING BIDS 33 partner having bid 2-No Trumps over your shift of 2-Spades from i-No Trump. 4 KQJ84 v 97632 4* A6 0 5 Spades and hearts (Also diamonds and clubs) having equal trick values are called "equal suits." First bid the higher of two "equal suits" (Spades before hearts or diamonds before clubs), if the two are of equivalent strength. First bid the stronger of two "equal suits" of unequal strength. An added trump in case you will speedily be ruffed often means a greater score. Z cannot be prevented from going game at hearts on the next hand, but perfect defense will save game at spades. 4842 V 82 4 A7643 I 875 4 K3 Y IO 75 V K IO 7 A B 5 3 4 95 4 KQJIo2 0 AKQJ62 Z0 IO9 3 4 AQJ96 v AQJ964 4 8 0 4 Prefer a 5-card major to a 6-card minor suit on account of the difficulty of making 5-odd. If you are liable to be ruffed a 7-card minor suit is better than a 5-card major suit. 34 CORRECT CONTRACT BRIDGE I Spade A A J Io 7 4 9 * 6 0 A J 9542 I Club a KQ862 v 3 4 KQ98762 0 --- When partner has aided your opening minor bid it is safe to show a very weak major suit, because partner can shift you back if he cannot properly aid your second suit. (On the hand shown below partner will aid your opening bid of i-Club, when overcalled by A's i-Diamond, then you may safely shift to 2-Hearts. Game can be made at the latter declaration but not at clubs). * KQ I v AQ84 * o 76 0 Io 5 4 4 A843 Y a J976 q2 IO2 A B q7 K 4 K3 852 OKQJ92 Z 08763 52 v J7653 * AQJ94 0 A After having shown your two suits, if they are of about equal strength, rebid your lower suit so that partner may shift to the higher without increase of contract; if your higher suit is the stronger you may rebid it to make that fact plain. (Rebid hearts on the first hand shown below but on the second again bid spades, after having in both instances shown both spades and hearts,) OPENING BIDS 35 * A Q io 9 5 K Q J 8 6 i 73 0 4 * A Q IO 9 5 4 K Q J 8 6 * 7 04 Unless you hold more than four sure tricks, so that others are too weak in commanding honors to bid, you need not fear that you will be unable to show your second suit. Through ability to establish your second suit or because you and dummy can cross-ruff losing cards in either hand, a two-suiter averages to win two more tricks than similar high cards would enable you to win without having a second long suit. A two-suiter averages to win three more tricks at the suit the better supported by dummy than the latter could win at no-trumps. Because opponents know these facts it is poor strategy to needlessly publish the fact that a two-suiter is held, as opponents will more strongly oppose what they know is dangerous than a supposedly moderately powerful hand. If partner satisfactorily supports your first suit shown, do not advertise a two-suiter. PREEMPTIVE BIDS A "preemptive bid" is one naming a game contract at a love score (3-No Trumps, four in a major or five in a minor suit) or one obliging opponents to bid game value at a love score (4-Diamonds is preemptive, since only a game contract can overcall it; 3-Spades is not preemptive as 4-odd in either minor suit can overcall; 4-Clubs is not really preemptive because it can be beaten by 4-Diamonds; it is common, however, to call such semi-shut-out bids "preemptive.") 36 CORRECT CONTRACT BRIDGE Preemptive bids require a minimum of two "sure tricks," like other opening bids; they also require the bi'dder to hold within two tricks of the amount declared, allowing partner to assist upon three probable tricks. Except as a defensive measure, a hand originally bid to its limit cannot be rebid even if partner assists. The opening two-bid used in contracting has no parallel in auctioning; it announces "game expectations and slam hopes," making it a stronger declaration than any preemptive bid not naming a slam. To a considerable extent contracting utilizes an opening two bid in situations calling for either a one or a preemptive bid in auctioning. Slams should rarely be attempted at no-trumps. Be careful to select the proper opening bid to best picture your hand to partner: the one bid to disclose little more than minimum strength; the two bid to announce game expectations and slam hopes; the preemptive bid to show little more than average defensive or assisting strength, and probable tricks within two of what you announce. Three no trumps ordinarily shows at least nine probable tricks held, regardless of the opening lead and of what partner holds. (See Chapter XXV for exceptional use.) 3 Spades A Q J 7 5 32 K 8 3 * 9 0 7 4 2 Spades AAKJ9643 95 4 KQJ 0 --- 2 Clubs 2 v A3 4 AKQJ862 0 KQ6 5 Diamonds - - - A *AK93 0 KQJIo8754 2NoTrumps KQJ v AQ84 * AKIo O K96 3NoTrumps a KJIo V A *AKQIo853 0 AQ VI OPENING BIDS THIRD OR FOURTH HAND REVOLUTIONARY as it may appear to Auction players, the requirements for opening contracting are identical for third and fourth hands. Either third or fourth hand may open the bidding upon any hand meeting the following minimum requirements: I. Two sure tricks held; 2. Ability to win a total of five tricks; 3. Ability to furnish five assisting tricks for partner's best declaration or to rebid; 4. Probable ability to safely outbid opponents or to prevent an adverse game, counting upon partner for a maximum of two assisting tricks or one defensive trick. Even if you hold as many as 3 2 sure tricks there are 82 in Ioo chances that partner holds at least one defensive trick. His chances to have two assisting tricks for you are still better. The above rules for opening the contracting are the most elastic yet formulated and also the most simple for anyone able to count "sure tricks" and "probable tricks;" without ability to readily count such values a player may as well abandon all idea of excelling at the newer game, whereat former methods of valuation are too crude and inadequate. 38 CORRECT CONTRACT BRIDGE A part score at Contract is a decided asset, justifying late opening bids probably incapable of going game, provided too strong defense is held to permit oppopents going game. Hands like those shown below stand excellent chances of gaining a stepping stone towards game, with minimum risk that opposing hands will be able to go game. iSpade * A K J 7 A K 6 4 963 0 8 2 I NoTrump Q J IO 4 A 7 3 * K Q IO OA75 An important feature to note is that considerable strength in both major suits lowers the total defensive strength needed to save game; comparatively small risk exists that opponents will be able to win 5-odd at a minor make after an adversary has passed. LATE MINOR BIDS Unless preemptive, a late opening minor bid denotes strong no-trump features with one weak suit. Instead of venturing no trump, a 4-card major bid, or an attempt to go game on his own best make, the minor bidder desires partner to make some tentative declaration to help determine the best final make for the joint 26 cards. iClub 4AK95 Z'AQ83 *KQJ6 03 i Diamond 4 --- A K Q 5 * K Q IO 4 0 A K IO 7 4 Partner of the minor bidder must do his best to aid the discovery of the best possible make for the joint hands. He may bid no trump upon probable stops in the three unbid suits; he may bid any 6-card suit, any 5-card suit headed by a single high honor, OPENING BIDS 39 or he may bid a 4-card suit of higher denomination if it contains two possible stops (A J X X, K J Io X, or even Q J 10 X). Length in the minor suit declared, with three assisting tricks calls for a raise of that declaration in case nothing better can be ventured. Of course definite acquaintance with your partner's particular notions concerning late minor bids may justify modification of the general rules given here. MINOR SUIT CONVENTIONS No secret code is allowed at the card table. All players are entitled to know the precise meanings of all conventions used. Bridge is filled with conventions to make play intelligible; most of these conventional acts are too well known to require explanation. Human ingenuity continually strives to discover some means of more clearly disclosing to partner the precise nature of cards held; being new to the great mass of card players Contract seemingly offers a rich field for such endeavors. Most of the conventions suggested are rejuvenated relics of a past decade, already tried and found wanting at Auction Bridge. In various small circles a host of differing uses of an opening i-Club or i-Diamond or of a 2-Club or 2-Diamond bid are being tried; each being termed a "minor suit convention," just as if each were the only act deserving that name. In one locality 2-Clubs means: "Partner, I hold two long minor suits; please choose between them." Two Diamonds means that two long major suits 40 CORRECT CONTRACT BRIDGE are held. In another place an opening 2-Clubs means strength in both black suits, while 2-Diamonds indicates a red two-suiter. In a third group of fans an opening minor bid of two means great no-trump strength with one very weak suit (presumably the suit declared, but possibly one of the major suits); the bidder's partner is supposed to bid 2-No Trumps in case he holds top honors in the minor suit declared, as the opening bidder must hold strength in the remaining suits; if the partner lacks sufficient top strength to identify the suit in which the original bidder is weak, then the partner must bid his best suit, or in case his best suit is the one bid he can assist that bid to show where his strength lies. To barely list the various minor suit conventions advocated would fill many pages. Some of them possess considerable merit and some are absurd. After eighteen years careful study of the possible utility of minor suit conventions I must admit that as yet I have not discovered a single one possessing sufficient merit to entitle it to a permanent place in the game. Amiable use of a harmless convention when among those employing it is courteous, but accepting any "minor suit convention" as a part of your regular game is at present inadvisable. VII OPENING TWO-BIDS yEARS before Contract Bridge had become So. ciety's Game, many Auction Bridge players had, without official sanction, adopted the custom of allowing 500 points premium for a little slam and IOOO points for a grand slam —just to liven up the game-when a slam was both bid and made. The great difficulty encountered in safely bidding slams by any method known to Auction's greatest experts finally resulted in a unique and more enlightening form of contracting; this system of bidding very powerful hands has been adopted by Contract players of long experience, under the title of "slam bidding." In its proper place there will be given all the fascinating details of the art of bidding for slams, also some of the less pleasing systems of bidding big hands. Do not be surprised if your Auction teacher raises hands of horror at the supposed sacrilege of being asked to scrap Auction procedure and to adopt new card values and more efficient methods of partnership bidding. From my own experience and what I have noted in the case of others I think that Auction players require from two to four years' constant Contract experience before they are ready to admit the superiority of "slam bidding." The first step taken towards a slam contract is an 41 42 CORRECT CONTRACT BRIDGE opening bid of two, thereby announcing: "GAME EXPECTATIONS; SLAM HOPES." Partner's average assistance is somewhat more than three tricks. Consequently a love score requires the declarer to hold a minimum of 6 tricks at no-trumps, 7 tricks at major suit makes, or 8 tricks at minor suit declarations, to justify any announcement of game expectations and slam hopes. The opening two-bid more often denotes surplus rather than bare bidding strength. To make certain that game may not be sacrificed through partner's failure to assist so significant a declaration, its bidder's partner must bid three in case he holds an ace or its equivalent (Either K Q of a suit or the K X of two unbid suits), although he holds only two small trumps. TWO NO TRUMPS The minimum requirements for making an opening bid of 2-No Trumps are: Four guarded suits containing 6 probable tricks, or 3 guarded suits with 7 probable tricks. Bid 3-No Trumps on any hand having 4 guarded suits if containing 9 safe tricks. NoTrump * KQ9 V A54 KJ7 O Io862 2NoTrumps Q Io8 V A J7 4 KQ I3 0 A Io9 2 No Trumps* AKJ v KQ io 4 963 0 AQ Io6 3NoTrumps AK V AQ4 LKQJIo9 OKQJ *Other systems of bidding such a hand are given later. Unless plainly marked in one partner's cards, OPENING TWO-BIDS 43 slams should not be attempted at no trumps, because slams are much more difficult and uncertain than at suit makes. The opening bid of 2-No Trumps ordinarily says only: "Game expected." A player holding all four aces in a hand counting ten or eleven safe tricks sometimes opens with 4 No Trumps or s-No Trumps, to show the precise number of tricks held, so that partner may bid a slam in case he holds enough of the missing kings. The first example given below was utilized for an opening bid of 4-No Trumps, partner raising to 7 -No Trumps upon his three kings. The second example was opened with 5-No Trumps and the declarer's partner bid a little slam. Declarer 4AQ VAQJ *AQio OAKQJio Dummy * K97 v K842 * KJ53 076 Declarer * A K Q V A K Q * A Q J OAQJ -Dummy *.454 V Io 9 6 3 * 8 4 2 OKI097 THE SLAM SIGNAL There are various systems of contracting powerful hands. Until otherwise announced we refer to "The Long Suit System" (The oldest and most simple method), which it is preferable to master first. An opening two-bid in any suit is termed "the slam signal." It positively announces game expectations unless partner is hopelessly weak; it ordinarily proclaims slam hopes; it obligates partner's assist upon a single ace or the equivalent value, even if partner lacks normal trump support. 44 CORRECT CONTRACT BRIDGE The minimum requirements for making an opening bid of two are: I. At least 5 trumps headed by the ace and probably incapable of losing more than a single trump trick (Either 5 trumps with 4 honors including the ace, or 6 trumps headed by A K Q, A K J, or AQJ); 2. Probable ability to win 7 tricks total at a major suit or 8 tricks at a minor suit. Fulfillment of even the minimum requirements insure game with the normal assistance of three tricks in partner's hand. Slightly above minimum holdings required for the bid insure game in case partner has the one trick required to assist. ISpade * AQJ53 V Io8 4 KQ7 0 K io8 2Spades * AKJ o6 v KJ9 485 0 A9 3 2Diamonds * 9 4 A7 K94 OAKQJ84 The slam signal may be given in three added ways: I. By making a forced bid one trick higher than required to overcall an opening declaration (As 2 -Spades over i-Heart), whether the opening bid is made by partner or an opponent; 2. By jumping partner's unopposed bid of one to three (Jumping i-Heart to 3-Hearts or I-Club to 3-Clubs announces that a slam is thought possible); 3. By bidding a suit already named by an opponent, instead of directly aiding partner by raising his declaration (Partner opens with I-Heart; second hand bids I-Spade; in case you are very strong in partner's suit and also hold no losing spades you OPENING TWO-BIDS 45 45 may bid 2-Spades, instead of 2-Hearts, thereby announcing two things by a single bid-that you are so strong that you expect a slam at partner's make and that you guarantee partner against loss of tricks in the suit named by opponent. This is an important feature of slam bidding). SECOND USE OF TWO BIDS The primary meaning of an opening two bid, and the one that its maker's partner must hold until undeceived, is that the opening bidder has command of trumps, as well as holding sufficient side strength to probably insure game and make possible a slam in case partner is strong. In case overwhelming trump strength is held, without sufficient side strength to make a slam appear possible, a higher opening bid than two must be made. Sometimes very great total strength is held, rendering game a certainty with little aid from partner, but trumps lack slam probabilities, either because the ace is lacking or because there are dangerous gaps in the honors held. Such a hand justifies a second use of the opening two-bid, to discover whether or not partner holds at least one definite trick. Hands like those shown below call for such use of an opening two-bid. 2Spades 4 KQJIo63 g KQIo 4 4 — Kg6 2 Clubs 6 AJ 9 V K Q4 4 A Q IO6 5 2 0 5 2Hearts * QJ6 V2AJ9843 4AQJ8 0 --- As in all cases of compensated bids (General strength atoning for lack of the expected trump 46 CORRECT CONTRACT BRIDGE strength), somewhat greater strength is needed than for making an uncompensated trump declaration. THE REVERSE SIGNAL The player giving the slam signal is momentarily captain of the ship. His opening two-bid is the signal of full speed ahead. If he really means "game expected and slam hoped," he will start "showing aces" (Explained later) in case his partner assists. If the opening bidder holds only game probabilities, in case his partner assists the opening two-bid, the captain will give "the reverse signal," by bidding exactly game, instead of showing an ace. Naming just game, by either partner, means "STOP; game is the limit!" Upon receipt of the stop signal the partner must never venture to bid higher, unless he can see a slam in his own hand. TRUMP STRENGTH AND SIDE WEAKNESS Great trump strength, with little or no side strength, calls for preemptive bids of three in major or four in minor suits, provided partner does not need more than three tricks to assist. A preemptive bid always expects partner to hold two tricks in order to fulfill contract. 3 Spades 4 K Q J Io 7 32 v K Q 8 4 5 0 64 4 Clubs 9 V 7 4 4 AQJIo8532 0 A7 Neither of the above hands can go game with OPENING TWO-BIDS 47 fewer than three tricks' aid from partner, unless opposing cards lie favorably. It is important-vital to success at Contract-to master exact card valuation and the essential differences between holdings calling for opening bids of one, two, or those of preemptive character. VIII FORCED BIDS AN opening bid is called "a free bid" because nothing has preceded to obligate the voluntary announcement that among other things its bidder has at least two sure tricks' defense against any opposing trump declaration. A "forced bid" is one made over a previous declaration and does not claim ability to win two defensive tricks. Probably but not necessarily, forced bid strength includes at least one sure trick and the average help for partner of three tricks. If lacking those two elements of strength expected of an average hand the maker of the forced bid should be able to safely continue his contracting if overcalled by either partner or opponent, otherwise the forced bid is as useless as campaign promises. Of course any holding worth an opening bid of one is equally worth a forced bid of like amount. Any five-trick hand worth an opening bid may also be bid two over another declaration, provided in both instances that sufficient trumps are held to spare those needed for ruffing leads of an opponent's suit. The minimum requirements for a forced suit bid are: i. One sure trick; 2. Probable ability to win three trump tricks; 48 FORCED BIDS 49 3. Probable ability to fulfill contract, Few players realize the great importance of being able to win three tricks in declarer's own suit. Six of the thirteen tricks average to be won by trumps and only seven tricks average to be won in the three side suits. Unless the declarer knows that he can take at least three of the six tricks which trumps must win his bid is not wholly sound, as opposing trump strength probably will exceed that of his side-a most unfortunate condition, frequently leading to serious loss. Any trump strength held by dummy fails to atone for declarer's trump weakness, as dummy counts probable trump tricks as a part of his own assisting values upon which he will raise the contract. (A trump suit like K J 10 6 2 is worth just three probable trump tricks, while suits like either K Io 8 6 2 or Q J 8 6 2 average to be worth only 2 y trump tricks, rendering the latter too weak to declare unless strongly compensated by side strength, or as part of a two-suiter when partner has opened the bidding with I No Trump.) A hand asking less than average aid from partner to go game may be used for a forced bid without considering its defensive or assisting strength. (The hand shown below may be bid as high as 4-Spades, either over partner's or an opponent's declaration.) 4 QJ Io865432 V 3 4 7 6 0 4 IMPROVING PARTNER'S BID You "improve partner's bid" by shifting to a declaration requiring fewer tricks for game (As 50 CORRECT CONTRACT BRIDGE when you shift partner's minor make requiring eleven tricks for game, to a major suit declaration needing one fewer trick), or when you shift to a make at which the joint 26 cards of your side can win more tricks. Although you hold normal aid for either minor suit declaration, the next hand obligates an attempt to improve partner's i-Club or i-Diamond by shifting to i-Spade. * AKI052 64 4 i063 J97 The following cards require you to bid 2-Diamonds over partner's i-Heart. * 7543 84 4 75 0 AQJ72 Avoid the appearance of a selfish desire to become the declarer but give your partner all possible information which may tend to the discovery of the best final declaration. Even with normal aid for partner's i-Club declaration you may properly bid i-Diamond on 4 6 4 3 v 75 * K Io 4 O AKio64 Your partner's low bid and your own single assist offer almost no hope of game at clubs, but your display of diamond strength may possibly enable partner to safely bid no trump, because he knows that you hold guards in his very weak suit. If your partner opens with I Heart and you hold the hand shown below, your proper course is to aid his decla FORCED BIDS 51 ration rather than shift to another major make which probably is no better than his own: A K Io 6 4 K Io 4 4 6 4 3 0 75 A five-card spade suit as trumps is worth only i 4 tricks more than its honors are worth as aid to partner's best bid. If in the above case your partner has bid a five-card heart suit you gain nothing by shifting to Spades; you will lose by the change in case his suit contains six cards, because his long cards are worth 2/4 tricks more than can be won with another suit as trumps. But on account of the long card value of your six trumps you must shift partner's opening bid of i-Heart to i-Spade on the following hand: KQJ o63 V K85 4 53 0 74 Although you have normal assistance for partner's major suit declaration, you may shift to another make affording a high premium for honors held, provided you do not thereby decrease your side's chances for game or slam. Shift partner's I-Heart to 2-Spades: AKJ Io7 v K63 4 Q 8 5 0 K Shift partner's I-Spade to 6-Diamonds: A Io7 K 6 3 * A OAKQJIo4 Doubtless your partner has the K Q of the suit he declared but there is no evidence that he holds the missing v A. Were your hearts headed by the ace your best declaration would be 7-No Trumps, as your partner must hold as good as two 52 CORRECT CONTRACT BRIDGE side kings or a side K Q to have a sound opening bid; either of those side holdings would enable you to make a grand slam, with i5o honors for 4 aces. If unable to support partner's bid, a shift to notrump requires only one sure trick and two well guarded suits. (The next hand justifies i-No Trump over partner's opening bid for i-Heart.) * A J 9 7 53 * Q J Io 9 0 J 7 2 If able to support partner's minor bid, a shift to no trump requires either three guarded suits and at least one sure trick, or two guarded suits with two sure tricks (The first two hands given below justify shifting i-Club to i-No Trump; the third hand makes preferable assisting partner's club bid). 4 KJ6 K Io3 * J64 0 Q I094 A KQ6 f A IO 3 4 J 6 4 0 8754 * AKQ v I083 * J642 0 754 Never advertise what you cannot deliver. A pass denotes weakness; a bid indicates ability to fulfill contract, willingness to be assisted, and either one sure trick held or holdings justifying further contracting in case your partner returns to his own make or doubles an opposing declaration. Shun the "rescue bids" sometimes advocated when partner bid an Auction Bridge no trump; it is worse than useless for a man who cannot swim to jump overboard in an attempt to rescue someone who can swim; on a par with the fruitless attempt to rescue from the water is the attempt to rescue partner from no trump when you have a trickless hand. If FORCED BIDS 53 fourth hand is strong he will take your partner out of no trump but your attempted rescue may be aided by your partner, doubled by an adversary, and result in serious loss. No hand can be too strong to take partner from no trump into a major suit declaration. Probable game at a minor make also justifies shifting partner from no trump. Knowledge that you never shift partner when hopelessly weak gives him courage to do whatever his cards justify attempting. Strong reasons for desiring to shift partner's declaration are being very weak in the suit he bids, or in case he bids no trumps, a void suit, a low singleton, or two worthless doubletons make it desirable to notify partner that a sound suit declaration may be safer than his no trump. In Contract your partner will either alter your shift of declaration or he will jump it. You must be prepared for any action that partner may take. In case he shifts your call you are expected either to hold at least one sure trick or be able to rebid your hand; if he jumps your bid within a single trick of game you should hold sufficient strength to warrant naming game. Any shift of partner's declaration that does not come up to above specifications is more liable to result in harm than probably will result from passing his bid. When lacking a single sure trick you may take partner out of no-trump on a single long suit worth at least three trump tricks, provided your hand is worth at least five tricks total (Overcall partner's I-No Trump as shown below): 54 CORRECT CONTRACT BRIDGE 2 Spades KJ Io8643 v 5 4 9 6 4 0 75 2 Hearts 4 K 6 C' Q9 7 6432 4 8 3 0 4 2 2Clubs * 5 q Q Io7 * Q Io8753 0 Qio6 A no-trump bid shows strength in at least three suits. Your partner may be obliged to rebid no trump because he is weakest in your best suit, but in case you hold a two-suiter he must be able to properly support one or the other of your suits; on this account it requires less strength to bid a two-suiter than to show a single long suit over partner's no trump. The minimum requirements for taking partner out of no trump with a two-suiter are: I. Each suit worth three probable trump tricks or one suit worth four trump tricks; 2. A hand worth four tricks total. You may make the bids indicated below over partner's i-No Trump, and in case he bids 2-No Trumps you may show your second long suit. 2 Hearts --- -- Q 98542 4 4 < J To 8 6 4 3 2 Clubs * 7 G Q 5 4 QJ Io764 0 QJ965 Note the following exception to the rules for taking partner out of no trump: when you hold the entire strength in a long minor suit your partner's no-trump should show at least one safe stop in each remaining suit; unless you have something towards game score you should bid 3-No Trumps rather than show minor suit (Bid 3-No Trumps on the next hand, instead of bidding diamonds). 6 4 8 5 4 Io 72 0 AKQJio6 FORCED BIDS 55 PARTNER'S PROBABLE A S SI STA NCE Every declaration a player makes obliges him to estimate the probable value of his hand, also to make some assumption concerning the probable aid to expect from his partner. The average holdings of a player who cannot bid, and the minimum required in commanding honors to venture specified declarations afford the only sound basis for estimating the probable assisting value of partner's hand.. Count upon partner for assistance as follows: 6 tricks if he opens the bidding with 2-No Trumps or in case he doubles a no trump at his left; 5 assisting tricks if he opens the bidding third or fourth hand, or in case he doubles a no trump at his right, or if he doubles a major suit declaration on either side; 4 tricks if he opens the bidding as dealer or second hand, or in case he doubles a minor make; 3 tricks if he has not bid; 2 tricks in case you hold a freak hand; no probable assistance if he fails to declare after you have repeatedly bid. If your partner has not declared, the hands given below are barely worth the forced bids indicated: I Spade 4 A J 9 6 4 K 72 6 4 0 Io85 2 Hearts a 75 v Q J Io 83 4 A J 5 0 K 94 3Clubs & 3 V 64 4 KQ97543 0 QJ6 Pass A Io8642 v 7 5 4 8 3 0 964 The last hand shown above may be bid to warn partner of lack of normal aid for an opening heart or club declaration or to improve his I-Diamond, 56 CORRECT CONTRACT BRIDGE although you cannot rebid if partner aids you. The hand is barely worth four probable tricks; it contains only a single defensive trick and has merely i 34 tricks' aid for partner's best make, rendering the hand much too weak for a forced bid in case your partner has not already declared. FORCED NO-TRUMP BIDS If your partner has already declared a suit offering poor chances for game, you may overcall an adverse suit make with no trump on either: I. One sure trick, two stops to the adverse suit, and a total strength of four probable tricks; 2. Or two sure tricks, a single stop to the adverse suit, and a total strength of five probable tricks. If your partner's opening I-Heart has been overcalled by i-Spade, either hand shown below may be bid I-No Trump: 4 KJ io8 v 7 K J 6 5 0 J IO96 * K Io 3 V 64 4A AJ Io7 KJ Io2 Weak hands require stops to the three suits not bid by partner. Two stops to the adverse suit and a readily establishable minor suit probably incapable of going game, or an established minor suit with only a single stop to the adverse suit, justify notrump although you cannot stop the run of one unbid suit. In each case shown below you may bid I-No Trump, partner's opening bid of i-Heart having been overcalled by I-Spade. A J Io 84 4 K Q J o6 0 J76 * Kg6 VC 5 * o183 0 AKQJ92 FORCED BIDS 57 If partner has not bid, the minimum requirements for I-No Trump over an adverse suit declaration are: (I) Two sure tricks, two stops to the adverse suit (Spades in each illustrative hand), four guarded suits, and probable strength of five tricks; KQJ K8 K J 9 4 0 J Io95 (2) Or two sure tricks, a single stop to the adverse suit, four guarded suits, and probable strength of at least six tricks; K72 v K6 4AJ65 OKQJ7 (3) Or a single stop to the adverse suit, three guarded suits, including a thoroughly established minor suit probably incapable of going game; K7 VA5 4AKQJ8 9763 A partial game score is almost useless at Auction, because almost invariably the next score will mean game without the previous one or else the other side nullifies the part game score by themselves going game. Especially when vulnerable, a small previous score is a decided asset at Contract, obviating the need of contracting for Ioo points to go game. Even when opponents cannot go game against you, probable ability to score a part game justifies taking a limited risk. The desirability of a stepping-stone towards game often induces a sound bidder to at once declare a hand probably unable to go game, whereas a less skilled player will pass, hoping that 58 CORRECT CONTRACT BRIDGE he may later on collect a penalty from an opposing overbid. As will be later on discussed, no-trump strength when partner has not bid frequently offers a choice between an immediate bid and the use of an informatory double, obliging the doubler's partner to declare his best make. In general, short major suits, without pronounced weakness in any suit make an immediate no-trump preferable to an informatory double of an adverse suit make. BIDDING AGAINST NO-TRUMPS Bidding for a lead against no-trumps is one of many situations requiring abandonment of Auction theories. Contract is a newer and deadlier species of warfare, utilizing more modern and scientific weapons. One of the most deadly gases to use against a contract for a part game score is SILENCE. A partial game score is valuable, but unless you can make at least a small score with small risk and are also certain that opponents cannot shift into any game-going declaration, it is puerile to bid for a lead against no-trump in case its bidder's fulfillment of contract cannot score game. Never disturb a satisfactory situation unless certain you can improve it. Watch the score, as you were never called upon to do at Auction, to note whether a fulfillment of contract will yield game; also carefully consider the probable result of each possible course open to you. The following hands will serve to illustrate the FORCED BIDS 59 analysis required by a player when no-trump is bid at his left. 4 Q 10 9 3 V 6432 4 0 Q432 4 876 Y 4542 Io975 A B V J8 4 832 4 AKQJ65 0875 Z OA6 AKJ v AKQ 4 I0 9 7 O K J Io 9 Z's opening bid of either I-No Trump or 2-No Trumps cannot be assisted by Y. Unless the I-No Trump means game if made, B must not even consider bidding his clubs. If fulfillment of that small contract will yield game, B has the option of remaining quiet, hoping that he can defeat the contract because seven tricks may not be won before someone leads diamonds or B may heroically bid 4-Clubs, be doubled and go down three tricks; this would be a small price to pay under some conditions of score and a heavy one under other conditions. Should Z open with a bid of 2-No Trumps, whether or not fulfillment means game, B is not called upon to bid-his chances are too good to defeat the contract. Y can go game at spades if B affords Z an 60 CORRECT CONTRACT BRIDGE opportunity to double clubs. B should suspect that game may lurk in one or the other major suit. If played to the best advantage Z is barely able to make one-odd at no-trumps. * Q o 8 7 2 9852 * 853 0 K6 4 62 Y 4 A 54 v843 A KQ6 4 Q9764 B K Io 2 0 975 Z I0 4 3 2 4 KJ93 v3 A J IO * AJ 0 AQJ8 Unless i-No Trump means game on the hand shown above, Z must open the bidding with 2-No Trumps, which can just be made, as A-B will win four club and one spade trick before Z can establish his spade. Four-odd can be made at spades but that declaration cannot come about unless some declaration by his opponents affords Z an opportunity to oblige Y to declare his best suit. B's values are insufficient for a double of I-No Trump at his left but in case that contract will yield game he may at least consider the probable result of obliging his partner to make a sacrifice bid; as the cards lie it would be bad. FORCED BIDS 6t CONTRACT AND AUCTION STRATEGY DIFFER Until their attention has been called to the numberless points wherein Contract strategy differs from that of Auction, even the most astute players of the older game constantly use incorrect Contract strategy. The following hand illustrates one such instance in bidding. 4 K Q 9 7 3 v A6 * QJ9 5 3 / 42 Y A AJ 5 A J987 A B KQIo3 4 642 B * A7 0 J964 Z AKQ5 4 86 v 542 4 K Io8 O I 8 7 3 2 Unless a club is the opening lead B can go game at no-trump from love score. Four-odd can be made by A at hearts, in case opponents bid and afford B an opportunity for an informatory double of one of the black suits. Y can make three-odd at spades. At either Contract or Auction the first three players should pass but at either game and at any score B should open the bidding; unless there is a high score B's opening bid at either game should be 2 No Trumps, which A cannot properly assist even at Contract. 62 CORRECT CONTRACT BRIDGE As 2-No Trumps at a love score will not yield a game at Contract, Y must pass. But at Auction the declarer can score all tricks made above the first six, so that Y dare not pass. Whether Y bids 3 -Spades, hoping later to show his clubs, or takes the bull by the horns and bids 4-Spades depends upon his personal ideas. B's double of 3-Spades will force A to bid 4-Hearts, which will yield a game, or else Y's overbid will be doubled, and suffer a penalty. BIDDING AGAINST NO-TRUMP AT RIGHT "Senior" makes the opening lead. Unless the iNo Trump or 2-No Trump bid will yield game, or unless he can make a strong informatory double, senior is seldom called upon to overcall a no-trump. Possession of an established suit renders a no-trump the most deirable make for senior to oppose. Unless he has game-going strength there are only four general types of hands that uniformly call for a player to overcall a no-trump at his right. I. If unable to save game against a probable shift of make, bid game on any freak suit capable of going game with about average aid from partner: 4 Hearts * 6 ' AKQo 9 6 5 3 4 8 4 0 73 5 Diamonds --- q 54 A J9 A 0 AKQIo8743 A suit of freak length ordinarily means some length in the no-trump hand and voidness or a singleton with his partner, so that the latter will make an endeavor to overcall the no-trump; if this can be FORCED BIDS 63 done and the no-trump hand can strongly support the make, you will find opponents able to outbid you. Anticipate such an event by preempting over the no-trump, so that the player at your left may be afraid to venture overcalling so high a declaration. 2. If probably able to save game against any shift of make, bid a hand no higher than needed to picture it to partner, if somewhat more than average aid is required to go game: 3Spades A K Q J I0 6 v A Io87 * --- 0 763 2Hearts * A I0o98 v"AKQI07 464 085 The 3-Spade bid is to allow partner to assist upon three probable tricks; the 2-Heart declaration shows that partner should not assist upon fewer than four probable tricks, unless an adverse overcall ensues. Either of above hands probably will win three defensive tricks against either minor suit declaration and either hand will probably win four tricks in case opponents shift to the unbid major suit. As there is small danger of a game-going shift being made by third hand you may as well try for a part game score, even if your partner cannot safely carry you to game. You are not called upon to allow an opponent to walk over you, just because he is able to bid no-trump. 3. Anticipate third hand's probable shift, by overcalling no-trump with any strong two-suiter: 2 Spades * A Q IO 6 5 v K J IO 7 4 * --- 0 8 7 4 4Spades 4AK97653 A --- 4KQJIo5 0 5 The first hand shown above indicates that third 64 CORRECT CONTRACT BRIDGE hand has greater than average probability of either holding a minor two-suiter or a freak club suit; one reason for bidding the 2-Spades is to insure an opening lead of that suit in case contracting runs to game heights before you can show your second long suit. It is possible but improbable that the last hand shown above can go game at clubs but not at spades; it is much more probable that a strong opposing bid will be made in case you make a low spade bid, intending to later show clubs, so you should follow the course that appears most likely to permit you to become the declarer, by preempting with 4-Spades. 4. If possible, even though improbable, that you may fulfill your contract in case partner can win two tricks, you may preempt with a defenseless hand: 3 Spades KJ Io 8 7 5 42 p -- - 9 6 5 0 42 4 Hearts 4 6 K I9 7 65 4 32 7 4 8 The assumption that it may be possible for the first of above hands to win seven trump tricks, or for the second hand to win eight heart tricks, is based upon the reasonable chance that in each case the missing Q lies in the no-trump hand and that entry to partner's hand will enable a single lead of trumps to be made through the holder of the missing Q. While in certain instances game actually results from such daring bids the chief reason for making them is the probability that game may be saved at small loss. The next hand shows a case where game actually resulted from a bid of 4-Spades over an opening bid of 2-No Trumps. FORCED BIDS v K 8 7 6 2 I 09 5 2 0 KJ3 4 Aio9765432 Y J ' - A B 9543 76 B KQJ 3 0 52 z IO 8 7 4 A KQ8 V AQJ A84 0 AQ96 With the possibility of making game in case B could win two tricks, A overcalled Z's opening declaration of 2-No Trumps with 4-Spades, which shut Y off from bidding hearts. Y's violation of the precept to lead your best suit when partner has bid no-trump lost game; instead of leading his hearts Y led a club, thereby establishing that suit in dummy. Z's return lead of hearts was ruffed by A, who led his only remaining club, then he discarded one of his losing diamonds on another lead of clubs. The declarer next led dummy's lone spade, upon which Z "split equals" by playing the Q and the trick was won by the ace. Up to date the declarer had lost only one trick; he had then to lose a single spade and one diamond trick, just giving him game. Y could have made a little slam at hearts, by establishing in Z's hand one spade and one diamond upon which to discard two of his losing clubs, finally giving his adversaries a single club trick. IX INFORMATORY DOUBLES THERE are "informatory doubles" and "business doubles. The first ask partner to make his best bid, unless he can defeat the doubled contract for greater gain than can result from any responsive bid; the second species of double asks partner to let the doubled contract stand, unless he can go game by bidding. The informatory doubler assumes all responsibility for the result of his partner's answering bid. Weakness is no excuse for failure to make a responsive declaration. Too few informatory doubles are employed at Contract; sometimes Contract games move too rapidly for an Auction brain to act logically, opponents snapping into a bid of 2-odd or 3-odd, whereas an Auction bid of only one might have been made. In many instances Auction rules for making informatory doubles are insufficiently comprehensive to cover Contract situations; players fail to make doubles that would give partners enlightening clues and opponents are allowed to get away with a contract not belonging to them. Don't let this occur. If you have proper doubling values, double. The requirements for a double to be informatory are: 66 INFORMATORY DOUBLES 67 67 i. It must be made at the first opportunity afforded to make any double; 2. Doubler's partner must neither have bid nor doubled an opposing bid; 3. The bid doubled must not exceed: i No Trump; 3-Hearts or 3-Spades; 4-Clubs or 4-Diamonds. All other doubles mean "business," and are intended to collect a penalty. Never mind what you did at Auction or what an Auction teacher informs you should be done at Contract; this is another species of game, requiring its own appropriate procedure that follows special basic principles. BASIC FACTS TO CONSIDER Sound procedure must be founded upon proven facts, all else is mere theory. When the twenty honors of the pack are each properly guarded, their aggregate value is i6 probable tricks. An average deal, leaving a part of these honors imperfectly guarded, yields I5 probable honor tricks. If North and South become the declarer and dummy, their honors of suits not bid by an opponent will average to yield full face value; honors held by East and West shrink to their sure trick or positional values. During the progress of contracting each side counts its probable offensive tricks; after the final contract has been awarded only the successful pair continues to count its bidding values. When one player opens the contracting and an 68 CORRECT CONTRACT BRIDGE other player doubles, each of the two remaining players temporarily is credited with having one-half the honor strength not required by the bidder and the doubler; in addition, the doubler's partner averages to have I Y2 tricks in low cards of his best suit. An opening bid of I-odd in any suit, or of 3 -odd in a major suit or 4-odd in a minor suit, require so little side strength in honors that on an average the partner of one making an informatory double has at least three tricks total, requiring the informatory doubler to furnish the balance of the tricks needed to fulfill the contract forced from the doubler's partner. Informatory doubles that adhere to these basic facts are sound and must average to produce favorable results. An analytical mind requires no set rules for making a sound informatory double of any opening bid. Suppose that you contemplate making an informatory double of I-No Trump. If that bid has been made at your left it cannot go game except from an adverse score of at least 65 points; any lower score does not justify a double unless you believe that your side can go game, or unless your values make it probable that you can score something safely and that you can collect a substantial penalty in case opponents try to outbid you. In case the i-No Trump is made at your right you face an entirely different situation from when the declaration occurs at your left. An opening bid of I-No Trump rarely shows more than 6 honor tricks; suppose that you hold 5 honor tricks and have a hand well able to support any response by your partner, or else you INFORM A TORY DOUBLES 69 are able to shift the one possible unfavorable response to something sound; the joint honor tricks held by the opening bidder and yourself total only 11, leaving 4 tricks to be divided between the two remaining players. Your partner will average to hold 2 honor tricks, plus his i 2 trump tricks, so that your 5 assisting tricks and his own strength should enable him to win a total of 8 or 9 tricks, and you have called upon him to bid only 2-odd. If you hold nothing beyond the minimum required to make your double you should not aid your partner's responsive declaration, unless he makes an unnecessarily high bid, to show that he expects game in case you have all that your double advertises, in which case you should bid for game. When considering making an informatory double, first consider how many tricks your partner must win to fulfill the contract into which you force him: a double of I-Heart gives your partner only I in 3 chances that he can bid I-Spade; probably he must bid 2-Clubs or 2-Diamonds, requiring him to win 8 tricks, of which you must furnish all except 3. Doubling a bid of an opponent at your left, raised to 2-Spades at your right, obliges your partner to bid 3-odd, and you must supply 6 assisting tricks as a minimum. In case you double an opening bid of 3-Hearts or 4-Diamonds, the most probable response must be 4-odd and you should hold no fewer than 7 assisting tricks. All of the bids thus far referred to afford average chances for you, partner to have at least 3 tricks in his own hand. An opening bid of 2-No Trumps, however, shows on its face 70 CORRECT CONTRACT BRIDGE that its bidder holds at least 6, more probably 7, honor tricks out of a probable total of 15, leaving not more than 8 or 9 among the three other players. Except in an emergency the doubler should at least be as strong as the player whom he doubles; if this is true in your case, what can your partner be expected to hold in honors? Probably he will have great difficulty in fulfilling his contract, let alone going game. That is why a double of 2-No Trumps must be considered as meaning "business." In making informatory doubles the vital factor is furnishing your partner sufficient aid to probably enable him to fulfill his contract, the number of sure tricks held is of secondary importance. Largely because the majority of Auction players cannot value a hand closely, rules for doubling in the older game stressed the number of sure tricks required, taking care to insist upon enough sure tricks to ordinarily give sufficient assisting tricks as well, although there is no necessary relationship between defensive and offensive values. In Contract Bridge, if you will note that no informatory double is attempted without holding at least 2 sure tricks and also the necessary number of assisting tricks, on all the informatory doubles yet mentioned you need not worry about the precise number of sure tricks required for this and for that particular double; the number of sure tricks beyond two will take care of itself. One bid frequently encountered in Contract"the slam signal," either as an opening bid of 2-odd or as a jump by the opening bidder's partner from INFORMATORY DOUBLES 7I i-odd to 3-odd-is unknown to Auction players. The opening two bid, announcing "game expectations and slam hopes," shows a minimum of 7 tricks at a major suit or 8 tricks at a minor suit, and requires careful consideration. So also does the third hand "slam signal," made by jumping the opening one bid to three, showing a minimum of 6 assisting tricks for major suits or 7 tricks for minor suits as being held by the opening bidder's partner. DOUBLING SLAM SIGNALS So many fine' Auction players are unaccustomed as yet to Contract that many of them still follow procedure of the older game, merely bidding up to whatever contract they believe prudent. For example: "trick-counters" open with a bid of 2-Spades to show a 6-trick hand; they do not shout "game expected, slam hoped." Against such a bidder you may assume that your partner will hold 3 tricks and that all you require for a sound informatory double are six assisting tricks, to enable your partner to fulfill a contract of 3-odd in his best suit. Or suppose that third hand jumps the opening bid of I-Spade, to 3-Spades, all that is indicated is that he shows five assisting tricks; he does not show slam hopes. To double this last declaration fourth hand needs only 7 assisting tricks, relying upon second hand to furnish his average of 3 tricks. Knowing just what opponents mean by their bids greatly aids an informatory doubler. The more dangerous doubles come when you encounter more 72 CORRECT CONTRACT BRIDGE modern methods of contracting, especially of unfamiliar systems. The follower of any strictly Contract method of bidding will at times make an opening bid of 2-odd on a practically solid trump suit, with some side strength. Followers of "The Short Suit System" or "The No-Trump System" (which will be explained later) also employ an opening two bid to show 5 sure tricks; such great defensive strength ordinarily means that the partner of an informatory doubler cannot be expected to have more than 2 tricks, the doubler must furnish the balance-7 assisting tricks for an opening bid of 2-Spades or 8 assisting tricks for a bid of I-Spade jumped at the doubler's right to 3-Spades. It will indeed be rare for a doubler to hold such remarkable strength against honest bidders, but such opportunities to double do occur, as shown by the following hands. IO 75 c 98 * J Io 7 o K6432 2 Y 964 Q K Q Io 6 A B J 5 4 3 2 4 AQ8 5 4 932 OAQJ7 z < io5 A A Q J 7 3 Io 5 4 AKQJ83 v A7 4 K64 098 INFORMATORY DOUBLES 73 73 Z opened the bidding on the above hand with 2 -Spades, giving A something to consider. He had 8~2 assisting tricks for any response by B. A did not anticipate defeating Z's bid but he knew that Y probably could not assist, as third hand could not have the one definite trick required for an assist; although Z bid 2-odd on short suits on hands containing 5 sure tricks, in this particular instance A's hand clearly showed that Z was bidding on a long and nearly solid suit, probably with the side Y A and one or both the missing minor kings; as Z happened to be a very conservative bidder A felt confident that Z was not bidding without the missing ace and at least one of the minor kings, otherwise A would not have felt so certain that Y might not assist. Had there been an advanced score A would have felt compelled to double; at the love score the informatory double was something of a gamble, with odds 2 to i that B could not bid hearts; even if B could make that major response there was no certainty that game could be made. A's hand counted 7 honor tricks, with ~2 trick for 4 trumps, plus at least one trick for ruffing spades; a total of at least 8~2 assisting tricks made it reasonably certain that something could be scored towards game, so A doubled. When B made the unexpected bid of 3-Hearts, A raised it to 4-Hearts and B went game. The hand below shows a sound informatory double of a third hand slam signal in a major suit. When it is comparatively unimportant to one player which of three suits becomes the trump, an informatory double allows partner to choose. 74 CORRECT CONTRACT BRIDGE 4 J 10 7 5 4 v KJ6 98 0 AK5 4 982 y - v 953 A A Q I72 4 KIo432 A B AQJ7 0 97 0 Q J o 8 4 AKQ63 v 84 4 65 0 6432 As frequently happens, Z made a minimum opening bid of i-Spade, which Y jumped to 3-Spades on a 634 trick hand, expecting game and perhaps a slam. Sitting back of the strong hand, B doubled on 834 assisting tricks, rather than bid 4-Hearts. Z passed, and A responded with a bid of 4-Clubs, which B raised to 5-Clubs; which contract A fulfilled, losing two diamond tricks. Note that sitting back (at the left) of your stronger adversary affords a favorable doubling position, averaging to require one less trick for safety than when you sit in an unfavorable doubling position with the strong opposing hand at your left. RULES FOR INFORMATORY DOUB LES You may stretch a point when an opposing declaration will yield game at the existing score. At love score, the minimum requirements for making INFORMATORY DOUBLES 75 informatory doubles are: two sure tricks, strength in at least three suits, andI. To double a minor make of i-odd, 4 assisting tricks (aside from trump length or ability to ruff): Double i-Club 4 K J 8 3 v A io 7 5 * 5 0 K 7 32 2. To double i-Heart or i-Spade, 5 assisting tricks: Double i-Heart 4 A io83 vq 7 4 KJ62 0 KQ54 Double i-Spade - v K Q Io 6 4 A J 7 3 0 K 9542 Note that such ideal distributions give in addition to the honors needed for the doubling strength, 32 trump trick for 4 cards of partner's suit or one full trick for 5 trumps; also that one trick additional may be counted for ruffing the opposing suit with 4 trumps or 2 ruffs with 5 trumps. This added strength often justifies a raise not indicated by your honor values. 3. To double i-No Trump at right, 5 assisting tricks: Double I-No Trump A KJ6 <y A93 Q I 5 4 0 A72 4. To double i-No Trump at left (only with a dangerous score), 6 assisting tricks: Double I-No Trump Qio92 v KQ7 *AJ6 OA85 5. To double a bid raised at your right to 2 -Spades or 2-Hearts, 3-Diamonds or 3-Clubs, 6 assisting tricks: 76 CORRECT CONTRACT BRIDGE Double 2-Spades 4 4 v KJ 97 A Q83 0 AJ I 5 Switch the suits as shown below and 3-Clubs may be doubled with no greater risk: 4AQ83 KJ97 44 0AJIo5 6. To double 3-odd in a major suit or 4-odd in a minor suit, 7 assisting tricks. The next hand affords an excellent illustration of the great utility of considering a double of 3-Spades as informatory. -A v AKQ8 4 KQJ73 0 A Q o 6 AKQio865 y 4 3 5 2 A B J IO 9643 4 84 4 A96 093 Z 0 J74 4 J9742 7 * IO 5 2 0 K85 2 My partner (Z) passed. A opened the contracting with 3-Spades. My hand (Y) counted 8 assisting tricks in honors alone; to this I had a right to add i 2 probable tricks for 4 trumps and one ruff of spades in case the response to my double came in either hearts or diamonds; if the reply came in clubs I could count a total of I I assisting tricksfar too great strength to miss trying for game, so I doubled for a responsive declaration. My partner carefully counted over her hand and then bid INFORMATORY DOUBLES 77 4-Diamonds, which I raised to S-Diamonds, as we had no score towards game. We could have col-lected 400 points penalty, had my partner chosen to leave in the double. At diamonds we won game, plus 50 points for over-trick, plus the first game towards rubber (this alone possesses an average value of 500 points), giving us a better score than we would have gained through defeating A. The only real objection that ever has existed concerning informatory doubles has been their misuse. Few players have understood the basic principles of sound informatory doubling. The doubler must have every trick that he advertises. On the next hand my partner made an informatory double of A's opening bid of 4-Clubs. My responsive declaration of 4-Spades gave us one overtrick. A business double of the 4-Clubs would have defeated A one trick, which would have been offset by the four honors held by A. A Q J Io 9 A AKQio 4 A 0 Q J IO 7 2 Y * 7 K76 KQJ Io7532B J 983 4e KQJI07532 ~ 94 0 A53 Z K964 A A8543 v 7642 4 86 0 82 78 CORRECT CONTRACT BRIDGE Of course all informatory doubles do not result in game, but if proper doubling values are held an opposing game may be saved at small expense, as the next hand shows. Y's double of A's opening bid of 4-Clubs resulted in B's double of the responsive declaration of 4-Hearts, but going down a single trick proved to be a saving over allowing opponents to make 5-odd at clubs.,A AQJ74 KQ KQ92 4 -o K Q J o 4 62 Y K Kio83 v Io 3 A84 4AQJ96543 A o * 82 0 A Z 0875 95 v J765 K7 0 96432 Of course it is rare to hold sufficient assisting strength, with an ideal distribution (5 4 4 o or 4 4 4 i) for making informatory doubles of 3-odd in major suits or 4-odd in the minors, but when such rare hands are held do not fail to use informatory doubles, first being assured that your partner will understand you. In Contract you need not worry about having to pass a major bid of 3-odd or 4-odd in a minor make, when you would like to double for business; neither declaration can score game from INFORMATORY DOUBLES 79 love; if you pass when you itch to double for business, if the declaration is assisted you can double the game bid and if the declaration is not assisted you will collect a small penalty undoubled. SUBSEQUENT DOUBLES A " subsequent double" is also informatory. The term merely means that the player who has opened the bidding, doubles an adverse declaration at the first opportunity afforded him, and that in the meanwhile the doubler's partner has neither bid nor doubled. The following hand calls for an opening bid of I-Diamond. In case partner bids I-Heart the hand is sufficiently strong in the three remaining suits to justify bidding I-No Trump. If an adversary bids I-Heart, the hand calls for a subsequent double, to inform partner that rebidding strength lies in side suits. If partner holds a fair spade hand the double is his cue to bid it; two stops in hearts and no strong suit justifies partner's bid of I-No Trump; less than normal trump support at diamonds calls for partner to bid 2-Clubs; lacking some better declaration he may assist diamonds. A J 6 2 v — l K Q I7 0 AQ Io85 A subsequent double always announces a hand of general no-trump type, presumably, but not necessarily, very weak in adversary's suit, as the great weakness may be in an unnamed suit. In each instance shown below the opening bid of I-Club and an overcall of i-Diamond causes preferred strategy 8o CORRECT CONTRACT BRIDGE to be an informatory (subsequent) double. In the first case you hope that partner may be able to respond with a major declaration; in the second case you hope that partner can bid spades, and intend to shift to no-trump if partner bids a heart. A A io 5 2 KJ I03 4 AQJ6 O 5 A AIO5 2 v5 4 AQJ6 O KJIo3 An opening bid of a major suit, made on a hand where rebidding strength chiefly lies in side suits, justifies a rebid in case an opponent bids one of your strong side suits, but if the opposing bid comes in your weakest side suit the subsequent double should be employed, as you cannot afford to be ruffed when you are rather short of trumps, unless your partner holds at least normal trump support. Either hand shown below calls for an opening bid of i-Heart; in case an opponent bids i-Spade you may rebid hearts with the first hand, but the second hand obligates employing the double. A QJ63 I' AKJ73 4 5 0 KQJ A 5 t) AKJ73 4 QJ63 0 K QJ With either hand the natural opening lead will be spades; the first hand will not be called upon to ruff the third round of that suit, thus conserving its trumps; the second hand will be forced to trump the second round of spades, as the hand contains only five trumps and lacks a side ace, trumps cannot be spared to ruff and still leave enough to pull down opposing hearts, unless its holder is certain that his partner has at least normal trump length, INFORMATORY DOUBLES 8i Except in one instance a powerful no-trump hand with one weak suit, justifies the use of a subsequent double; when your weakest suit is of lower value than the one adversely declared you must choose between bidding 2-No Trumps and passing; you do not want to be obliged to bid 3-No Trumps in case your partner's response to your double happens to be three in your weakest suit. Having opened the bidding with I-No Trump, the first hand below calls for a subsequent double of 2-Spades; the second hand justifies a double of 2 -Clubs; on the third hand you must either bid 2-No Trumps over 2-Hearts and risk your partner having some diamond strength or else you must pass; you do not want your partner to bid 3-Diamonds on a very weak hand. * 64 q) AJIo5 4 AQJ 0 KQio6 4 AK7 2 AQio * 853 0 AJ97 A AQ62 ` KJ io8 4 AQ9 0 76 More frequently than at Auction, unless you hope for game or unless you expect to push opponents beyond their safe limit of contracting, when an opposing declaration comes in one of your strong suits it may be unwise to bid or double, thereby affording your adversary a chance to escape to a make less favorable to you. Always carefully consider the score and other features before you act. REPEATING A DOUBLE An adverse declaration over an informatory double cancels obligation to respond to the double. 82 CORRECT CONTRACT BRIDGE In case you have sufficient strength to force a declaration from your partner you may repeat your informatory double. The following hand appeared when a small score meant game for either side, and illustrates the occasional great utility of the repeated informatory double: 4 43 v 764 4* I 9 8 7 3 0 873 4 Q98 Y 4 76 52 J9 A B Q853 -4 A 4 65 2 0 KQJIo942 Z 0 6 A AKJ io v2 A K o 4 KQJ4 O A 5 Had Z opened the bidding with i-No Trump of course A would have passed and defeated the contract, but A overcalled Z's opening bid of i-Spade with 2-Diamonds. Z made a subsequent double and A shut-out Y by going 3-Diamonds. When Z repeated his double it was still informatory and Y responded with 4-Clubs, and made 5-odd by establishing a spade in Z's hand upon which Y discarded a losing heart. DOUB LING EACH OF TWO SUITS To be informatory a double must be made at the first opportunity. You cannot pass one declaration because you like it and then double a shift of make INFORMATORY DOUBLES 83 that you do not like, without confusing your partner. You should anticipate the shift of declaration, making an informatory double of the first bid so that your double of the second declaration will also be read as informatory. An informatory double of each of two bids shows that you are strong in the suit first declared and weak in the second suit shown. If you are weak in the first suit and strong in the second suit you naturally prefer the latter make and so inform your partner by passing. Suppose that you hold the following hand when i-Club is bid at your right: 6 5 V AJ74 4 KJ96 0 AK72 Your best course is to double the i-Club, intending to aid your partner's bid of either diamonds or hearts, or to shift to i-No Trump in case your partner bids i-Spade. If i-Spade should be bid at your left you should double that second declaration, informing your partner that you are strong in clubs and fear only spades; upon receipt of your last message your partner will reply in diamonds or hearts if able to do so, or he may go i-No Trump if he has spades well stopped. ASSISTING DOUBLES An "assisting double" is one made by the partner, of the opening bidder. This double may be made of an adverse overcall of two in any suit, when partner's opening bid was I-No Trump. The object of the double is to show at least two stops to 84 CORRECT CONTRACT BRIDGE the run of the adverse suit, and four assisting tricks, to allow the original bidder to return to his notrump if he thinks game is possible, or to allow the double to stand for a penalty in case he thinks the value of the penalty may be preferable to a part game score. In case the partner of the no-trump bidder holds an established minor suit or at least five assisting tricks distributed among three or four suits, he should bid 2-No Trumps in preference to making an assisting double. Suppose that you hold each of the three hands shown below when 2-Hearts have been bid over your partner's opening bid of i-No Trump; proper procedure in each case is as indicated: Double 2-Hearts A AK7 v KJ IO8 4 986 0 Io62 Bid 2-No Trumps A 7 3 K J Io 8 4 KJ 6 0 o62 Pass * 9 7 3 v K J Io 8 K 8 6 O Io62 The first of the above hands justifies bidding 3 -No Trumps in case your partner shifts your double of 2-Hearts to 3-odd in either minor suit. The last hand requires you to bid 2-No Trumps if your partner doubles the 2-Hearts. If your partner's opening suit bid is overcalled by a low suit declaration you may be able to employ to advantage another species of assisting double. A strictly business double of a low make seldom pays well; unless you are prepared to double any shift of call your announcement of ability to beat one declaration ordinarily results in a shift of make, to INFORMATORY DOUBLES 85 the advantage of opponents. In case you are able to defeat any adverse declaration your side should have some game-going declaration that your partner will help you find if you notify him of your great side strength and inability to properly aid his first bid. The assisting suit double is removed from strictly conventional procedure, as any highly trained player will correctly interpret it without previous explanation. It offers a perfect picture of your hand for your partner's consideration. You must be lacking in assisting length of his suit; you cannot safely stop the run of opponent's suit, although you must hold at least four of its cards, as otherwise you must be long enough in some other suit to bid; you must hold nearly solid tops in the two unbid suits, otherwise you would not assure partner that his two defensive tricks plus what you hold in the two side suits insure opponent's inability to go game on fulfillment of a doubled contract; your assisting double states that opponents cannot make more than I-odd at a major or over 2-odd at a minor make, at the worst. Your assisting double allows your partner to rebid his suit in case he asks only side help from you; to shift to a second long suit, knowing that you hold most of its high honors; to allow the double to stand in case he neither desires to rebid nor to show a second suit; to go to no-trump if he holds stops to opponent's suit and prefers game to a penalty. After your partner's opening bid of I-Heart has 86 CORRECT CONTRACT BRI DGE been overcalled at your right, the following hands call for the action indicated: Double i-Spade 4 9632 52 KQJ OAKQ7 Double i-Spade Io 864 8 *AQJIo 0 KQio6 Double 2-Clubs 6 AKQ C 9 4 98643 0 AKJ7 Following your partner's opening bid and your double of its overcalls, he should proceed as indicated below: Bid 2-Hearts 5 V AKQJ7 4962 0 I0543 Pass 6 732 I AKQ6 * 97 0 A874 Bid 2-Diamonds 4865?AK743 4- Q8532 x RESPONSES TO INFORMATORY DOUBLES W HEN responding to an informatory double remember that you are not playing Auction. If your values plus those shown by partner's double indicate game, so inform your partner by your response, as illustrated by the following hand: AJ9 6 v 654 * A86 0 A I 4 & K5 Y * 73 V KQJ io8 A B v 732 ^ K 72 * J IO 9 3 Q75 Z 0 J864 4 Q o842 gV A 9 * Q54 0 K92 When Y doubles A's opening bid of i-Heart, made over Z's pass, the latter's proper response is 2-Spades, because Z's hand is worth five probable tricks at spades, which added to the five assisting tricks shown by Y's informatory double of i-odd in a major suit means game. Y having shown by his informatory double nearly all values held might 88 CORRECT CONTRACT BRIDGE hesitate to raise a responsive bid of only i-Spade, made after Z had already declined to open the bidding, but Y cannot hesitate over jumping his partner's unnecessarily high response to 4-Spades. As is ordinarily the case where hands count only a fraction of a trick more than game value, Z must play his cards very carefully to fulfill his contract. The natural (play, offensively and defensively, will go as follows: the opening lead will be A's v K, which Z must win. When dummy is tabled Z can tell that three cards of each minor suit in his own hand and also in dummy will make the hand hard to play for game; he knows that A must hold at least one of the two missing black kings to give him the two sure tricks needed to open the contracting; A may hold the 0 Q J X, for a part of his values, but more probably he holds both black kings. Z's proper return lead is his A Q; two leads of which suit bring down all opposing trumps. The declarer's next play must be to lead a losing heart, both for the purpose of stripping his hands of that suit and in hopes that A will oblige by making a return lead of either clubs or diamonds. Of course A will do neither, he will lead back a heart and force Z to ruff it. Holding in the two hands of declarer and dummy the particular combination of 0 A o1 4 and 0 K 9 2, Z knows that if he leads diamonds from either hand a trick must be lost in that suit, regardless of the location of the Q J; he also knows that unless both the Q J lie in one hand he will pick up all tricks made in diamonds in case an ad INFORMATORY DOUBLES 89 versary is forced to open that suit. Z must not touch diamonds; the only thing left for him to do is to lead a small club from his own hand, winning with dummy's ace. He must lead back a low club towards his queen, if B unexpectedly has the king Z will win two club tricks, but when he finds that A holds the high club he must yield his adversaries two club tricks, as A will return a club and B will win that trick. B is in a hole; he cannot lead another club without allowing Z to ruff in one hand and discard a low diamond from the other hand, so B must lead back his fourth-best diamond; Z will play low second hand but A sees that he must go up with his queen or lose the trick to dummy's Io. As long as both the Q J of that suit are not held by one player Z will win the balance of the tricks, just going game. GENERAL PRINCIPLES GOVERNING RESPONSES Ordinarily the result of an informatory double cannot be foretold by the doubler's partner, whose sole obligation is to make his most appropriate bid. A barely sufficient responsive bid is noncommittal (Requiring the doubler to hold greater values than shown by his informatory double to assist); a bid of one trick greater than necessary (As 2-Spades over a double of I-Heart) shows probable game strength (Allowing the doubler to assist in case the response fits his hand, although he holds no strength 90 CORRECT CONTRACT BRIDGE in excess of doubling requirements); a response two tricks in excess of that required (As 3-Hearts over I-Club) announces a very powerful suit, without much side strength (As 2 K Q io 8 6 5 2, with little or no side strength). Never guess at what the doubler wants; always note the state of score, consider previous bids made, then carefully value your hand at the various possible responses. Ordinarily a major suit response is to be preferred to a minor suit make worth an added trick, unless you have at least 20 points towards game. With the same strength at either make a major suit involves less risk than a no-trump, except when you hold either two stops to the adverse suit with average high side cards or a single stop to the opposing suit with better than average side cards. Different conditions at Contract render much of the procedure advised for Auction questionable, at best. Instead of giving you a long list of rules to apply to each of the possible situations that may arise, the very simple performance of adding together the assisting tricks shown by the double and those that you hold will enable you to make your best probable response under any conditions. The following examples illustrate the process to employ. Suppose that when you hold anyone of the hands given below your partner makes an informatory double of i-Heart and that you have no score towards game. In each instance your partner's double shows a minimum of 5 assisting tricks; also an average of one trick more for a suit than for a INFORMATORY DOUBLES 9I no-trump response. Also remember that an informatory double of a suit probably gives your fourth trump a slightly greater value than though your partner had not been able to double-a value of Y2 instead of the usual Y4 trick, giving your joint hands when you hold only 4 trumps a probable value of I 3/ more tricks at a suit than at no-trump. i. 4 Kio63 v A9 * AQ84 0 963 Hand i counts 4y2 honor tricks at any possible response (spades, i f4; hearts, i trick only, as an opponent has bid the suit; clubs, 2%4 tricks). In case your partner holds in honor tricks the full five advertised by his double, you jointly hold sufficient strength to go game at no-trump, provided your single heart stop will enable you to run off the full 9 tricks without having to let opponents in. But at spades your joint hands count a probable io tricks, regardless of a break in the continuity of your trick winning. On the whole a spade response is safer than no-trump, and you should respond with iSpade, as your hand is slightly below game certainty. Should your partner bid 2-Spades you should bid 4-Spades. If your partner will not raise you even once it is unlikely that game can be made. 2. 4 9 6 3 v A9 4 A Q 8 4 0 KIo63 3 Hand 2 counts as before 4y2 honor tricks at any make or a probable 5 tricks at either clubs or diamonds. Your adversary's opening bid advertised 2 sure defensive tricks; evidently one of these lies out 92 CORRECT CONTRACT BRIDGE side of hearts, probably in spades; you will be lucky if you can play the hand at clubs without having to lose a third trick. Apparently the prospect of going game at no-trump is slightly better than of doing so at clubs or diamonds, and I-No Trump appears to be the proper response. 3. 4 963 v KJ94 e J872 0 75 Hand 3 possesses little merit aside from the fact that hearts can be stopped two or more times, but the doubler can scarcely be expected to win all the side tricks required for game. The only reasonable thing is to bid 2-Clubs. 4. 4 865 q KJ I2 4 974 0 852 Hand 4 had better be bid i-Spade than i-No Trump, although the spades are only three in number and at least two stops are held to direct leads of hearts. Make it a rule never to bid no-trump in response to an informatory double unless you are willing that partner should assist that make and unless you are prepared to bid for game. 5. 4 9 v 862 * K9742 0 K864 Hand 5 calls for a response of 2-Clubs; should your partner bid 2-Spades you must bid 3-Diamonds, to warn him away from your worst suit; the fact that you chose to first bid a lower suit will clearly indicate that your diamonds are shorter than your clubs, allowing him an intelligent choice of action. INFORMATORY DOUBLES 93 RESPONSES TO NO-TRUMP DOUBLES Responses to no-trump doubles average to be less satisfactory than bids made in answer to an informatory double of a suit make; in the first instance it is unlikely that the doubler holds strength in all four suits and it is not probable that his lengths of suits are alike; an informatory double of a suit ordinarily means that the doubler can soon ruff leads of that suit and that the doubler holds some strength in any suit in which his partner responds. Unless your proper course is to defeat the doubled no-trump, you must respond as if the doubled declaration happened to be your weakest suit. For example: your partner doubles i-No Trump; you hold the following hand; reply with 2-Diamonds, just as if your partner had doubled i-Spade. 4 32 V K85 4 1653 0 Q974 When your hand is worth practically the same number of tricks at its best suit as at no-trump, an informatory double of i-No Trump offers three alternatives: I. At love score to let the double stand in case you have about 3 defensive tricks total, rendering it more probable that you will collect a penalty than that you can go game in case you assume a higher no-trump declaration; 2. In case 2-No Trumps will give you game when your hand is worth three tricks total you may 94 CORRECT CONTRACT BRIDGE make that response. If your hand contains more than three guarded suits and counts at least four tricks you may try for game at no-trump, if a game seems more desirable than a penalty collected from opponents; 3. Probable inability to go game at a minor suit justifies letting the double stand in case you can make the opening lead of an established or establishable suit, or in case you cannot make an opening lead of an established minor suit when holding sure side entry. Poorly distributed strength and any uncertainty concerning ability to defeat the doubled no-trump makes a responsive bid a necessity. THE BUSINESS PASS A "business pass" is made by the partner of a player making an informatory double of either a suit or a no-trump bid, when the doubler's partner makes no responsive declaration. The following hand illustrates this point. * J753 ' 974 4 Io 8 5 4 Q5 6 K98 Y 4 Q64 V KJ8 A B 2 A52 4 A63 Q72 0 A IO74 Z 0 9862 A A o 2 2 Q o1 6 3 4 KJ9 0 KJ3 IN FORMATORY DOUBLES 95 Neither side had any game score. Z opened the bidding with i-No Trump, which A doubled on 5 Y4 probable honor tricks. B held only 3 honor tricks and no suit worth bidding; his choice lay between bidding 2-No Trumps with the probability of going down in case A carried the declaration to game, or of letting the double stand for an almost certain penalty. B made a business pass, thereby collecting 200 points penalty. Had B bid he could have made only 2-odd at either no-trumps or at diamonds. RESPONSES TO SUBSEQUENT DOUB LES A "subsequent double" (One made by the player who opened the bidding) gives a better clue to its maker's desires than an ordinary informatory double. A subsequent double plainly says: "Partner, you may assist my original make; you may improve upon it; or you may let the doubled contract stand if you can defeat it for greater gain than can result from any other action." Partner's double may indicate weakness in the adverse suit or he may be strong in that suit but very weak in a side suit, so that he does not wish to venture bidding no-trump unless you respond with a declaration of the suit he fears. An opening minor bid, followed by a double, ordinarily shows strong support for any unbid major suit. An opening major suit make, followed by a double, shows lack of trumps for ruffing purposes, 96 CORRECT CONTRACT BRIDGE unless you can strongly support partner's opening declaration. A response in a major suit, wherein you can win three tricks, is preferable to supporting partner's opening minor bid, unless game seems possible thereat. A shift to the other major suit, provided you can win at least three tricks, is safer than aiding partner upon three small cards of his original suit or on a singly guarded high honor. In each case shown below your partner's opening bid is supposed to be I-Spade, then he has doubled an overcall of 2-Clubs, your response should be as indicated: Bid 2-Spades 4 963 V A542 4 K76 0 952 Bid 2-Hearts 4 864 2 KJ Io72 4 I0864 0 9 Bid 2-Spades K 7 5 2 A I0843 6 53 0 84 Bid 2-No Trumps 76 v KJ97 4 KJ IOS 0 Q73 Bid 2-Spades * 854 Q 8 4 62 0 AJ964 Your partner shows a hand of no-trump type by first bidding a suit and then doubling the I-No Trump declared over his tentative suit make; he is ready to adequately assist a shift to either of two of the three unbid suits, and he should be prepared for the chance that you may respond in his poorest suit. In case your partner's opening bid has been a minor one he evidently hopes for a response in a major suit. In case his opening bid has been a INFORMATORY DOUBLES 97 weak major suit call he does not care for you to aid it upon less strength than four cards or three including ace, king, or queen. VOLUNTARY RESPONSES A "voluntary response" is made when you bid over a shift of the original declaration which your partner has doubled, or when you respond to your partner's informatory double after the intervening player has "jumped" the original bid; in either case your obligation to respond to the double has been cancelled by the bid made at your right. Unless a sacrifice is intended because the adverse score is dangerous, a "voluntary bid" announces game expectations at Contract. It can mean nothing less, regardless of what your Auction teacher or favorite authority has to say on that subject at the older game. The following hand illustrates the use of the "voluntary response." 4 943 v 63 4 AJ o 7 2 0 Q o 8 4 AQ52 Y KJ Io86 K Io 5 A 74 4 96 A B *KQ53 AJ94 O 75 7 v2 AQJ982 4 84 0 K632 98 CORRECT CONTRACT BRIDGE Z made a sound opening bid of i-Heart; A's informatory double was sound and showed at least five assisting tricks for a response in at least two suits (Either spades or diamonds); Y's shift to 2 -Clubs was a questionable bit of strategy, as his pass would have shown lack of assisting strength for hearts. B's voluntary response of 2-Spades left no question in his partner's mind that game was probable and A ended the contracting with 4-Spades, which were readily made. Just because B felt satisfied that Y would not do well at clubs gave him no excuse for failure to declare spades. Had B passed Z would have rebid hearts and A would not have repeated his double; even had B bid 2-Spades on the second round A would hardly have ventured to raise that make, especially if Z failed to rebid, because B's failure to at once declare his spades would make it appear as if game could not result from a secondary bid. XI OVERCALLING DOUBLES IF you have nothing to say, when your partner's bid is doubled at your right, say it-by passing. If you are strong, let your partner know that by interposing a bid before a response can be made to the double. A sound informatory double, like an opening notrump declaration, warns you that game hopes ordinarily must be the limit of your ambition. Unless the very unusual nature of your hand causes a slam possibility to shriek in your ear, do not attempt slam bidding. Some warnings hardly can be repeated too often. Note the meaning of adverse bids as well as those by partner. If an adversary announces by an opening bid that he holds at least two sure tricks, or if he makes an informatory-double that shows a probable three defensive tricks, it is best to believe that he tells the truth. Show complete satisfaction with your partner's doubled bid and that you expect game, by jumping the contract to the limit of your strength, provided that does not exceed game. The following hand justifies jumping partner's doubled bid of i-Spade, to 4-Spades; although Y's hand indicates fulfillment of a contract of 5-odd such a bid is not advisable: 99 100 CORRECT CONTRACT BRIDGE 4 Q 9 8 5 4 v A2 K93 0AQ A7 V KQJ6 AJ65 0 KJ82 3 1 Io 8 7 5 842 0 O 7 6 4 3 z 4 AKJ6a ' 943 4 Q Io 7 0 95 If possible, shift partner's major suit declaration that you cannot strongly support, or his doubled minor make without regard to anything short of game support, to any declaration offering better game probabilities. In the first case shown below shift partner's doubled i-Heart to 2-Spades. The second hand calls for a shift of his i-Club to iHeart. The third hand suggests that you shift partner's i-Spade to 2-No Trumps. A Q o 9 6 2 2 4 2 K75 v KQIo86 82 v AJ7 4 K 4 K6 4 J74 Q9 5 0 A Io 5 Q7 AQ63 Unless your partner is a wholly unreliable bidder, trust what he tells you and believe in the values found in your own hand, rather than think that the opposing double will prevent you from going game. The hand given below shows the boldness with which a player must sometimes back his convictions. OVERCALLING DOUBLES IOI 4 J963 v AQ8 * Q 10 3 2 <>-K9 4 AQ5 Y 4742 2 K J 6 A B IO 10543 y J74 4 & 985 AIO 3 2 Z 0 876 4 K IO8 v 972 4 AK6 0 QJ54 Z opened the bidding with i-No Trump on a 5 -trick hand. A doubled on his 5 4 tricks. Y held four guarded suits back of the doubler and counted 434 probable assisting tricks. Y feared that Z might not venture bidding 3-No Trumps if Y gave only a single raise, so Y went the limit by bidding 3-No Trumps. With the doubler sandwiched between them Y-Z readily made 4-odd. It is rare for the original bidder's partner to be able to bid game over a doubled no-trump, but frequently he is called upon to bid 2-No Trumps, and even more often he may properly show a strong suit, which may go game, especially when only 4-odd is required; it is rare to make 5-odd against the doubler of an opening no-trump declaration. REDOUBLING A redouble must be of the same nature as the preceding double, whether the double is informatory or means business (Z may open with i-Spade; 102 CORRECT CONTRACT BRIDGE A may make an informatory double upon the following hand: A 5 v2 A Io 6 5 4 K Q 8 6 0 A J 9 7, stating that he has no-trump strength in all but one suit-presumably spades; Y redoubles on the following hand: O 6 2 9 82 4 AJ Io 7 O K Q 8 6, thus reporting that he has assisting strength in side suits, but his spades are insufficient to raise that declaration and that one weak suit prevents him from shifting to no-trump. The messages of both A and Y are perfectly clear; B must either bid or utilize "the informatory pass;" as the doubled and redoubled I-Spade almost certainly insures game. The redouble enables the original bidder to proceed with almost as great certainty as if his partner had shown his hand). Business redoubles seldom pay. The time has gone when a fake redouble frightened a timid opponent into rebidding, instead of passing and collecting a large penalty. If able to fulfill a doubled contract it is poor strategy to announce that fact by redoubling, thus allowing an adversary to rebid. THE INFORMATORY PASS "The informatory pass" is the expert's method of showing a worthless Cavendish hand (One divided among the suits 4 3 3 3) when his partner's informatory double is redoubled. If the redoubled bid is in a suit, the player making the informatory pass states that his only 4-card suit is the one redoubled and that probably no high honor is held in either one of his three 3-card suits. In case the redoubled bid is I-No Trump, the informatory pass OVERCALLING DOUBLES I03 states that the only 4-card suit held is a worthless minor one; the doubler's knowledge that at least three cards are held of each suit enables him to make the best declaration for the joint hands. The following hands held by the partner of the doubler shows what should be done under various circumstances: When the redoubled declaration is I-Heart: Pass 4 975 v' Io852 4 974 0 832 Bid I-Spade 4 9 7 5 2 O io 8 5 * 974 0 832 Bid 2-Clubs 4 975 ' Io85 49743 0832 When the redoubled declaration is I-No Trump: Pass * 964 V 852 * 9863 0 742 2-Spades 4 J865 V 852 4 963 0 742 2-Clubs 9 6 4 852 A 8 6 4 0 742 Whether the doubled and redoubled bid is in a suit or at no-trumps, the doubler's partner must carefully avoid passing when his hand is not a genuine Cavendish. Such a hand as the following obligates a response in one or the other minor suits, preferably bidding 2-Clubs —the lower of two very poor suits: 6 652 V 73 4 J972 0Q853 XII ASSISTING PARTNER A RELIABLE partner's opening bids must be accepted at their face values and aided accordingly; the same is true of forced or secondary bids, unless a low adverse contract will yield opponents game. Any sound bid of one-odd requires for fulfillment of its contract not more than partner's average support of three tricks; a suit bid also expects partner to furnish normal trump support of three small trumps or their equivalent. The declarer's partner may raise a sound declaration one trick for each trick held in excess of average assistance; stops are required in the assisting hand to any suit bid directly over partner's no-trump declaration. A sound preemptive suit bid indicates indifference to partner's trump support, relies upon partner for only two probable tricks for fulfillment of contract, and expects to be raised in case partner has three assisting tricks. The requirements for raising opening bids of two-odd will be found in Chapter XXII (Slam Signals). RULE OF FIVE Each unaided rebid by partner announces ability to win two more tricks than shown by his previous declaration, inviting your assistance upon one less 104 ASSISTING PARTNER Io5 trick than needed to raise his previous bid. To enable players to readily recall the number ot tricks required to assist an opening bid of one-odd, or an unaided rebid by partner, I devised the following: Rule of Five: Subtract from 5, partners last bid; the difference shows the number of tricks you must hold to assist. For example: Partner opens the bidding with i-Spade; you subtract I from 5, the difference is 4, showing that you need 4 probable tricks to bid 2-Spades. Suppose that you lack those 4 assisting tricks and that you pass; if your partner's bid is overcalled at your left by 2-Clubs and he makes an unaided declaration of 2-Spades; 5 minus 2 equals 3, showing that you require only 3 tricks to aid. Should you still be unable to assist, and should your partner next bid 3-Spades over 3-Clubs, application of the Rule of Five shows that you now need only 2 tricks to bid 4-Spades. CONTRACTING STRATEGY Ordinarily it is difficult to wean Auction players from early habits, so that they may thrive upon a solid diet of Contracting Strategy; they are prone to sulk because they are not allowed to open the bidding upon A K X X X, or some similar holding, to show the possession of two sure tricks, although the hand is below average strength, neither having probable ability to win 4 tricks total nor still less to yield the average assistance of three tricks for partner's best declaration. o16 CORRECT CONTRACT BRIDGE Early players of Auction knew so little about a pack of cards that they were trained by as crude methods as our Revolutionary ancestors employed with Continental Army recruits, with their historic wisps of hay and straw. In I915 one of the most important advances made in Auction was teaching players to roughly value dummy by doubling the value of its "quick tricks." Nowadays a player who at once assisted a dealer's opening declaration of one-odd, on two bare aces and three little trumps (Barely three probable tricks' support) would probably know that he was making an improper raise, one a full Q o1 short of average support. It ordinarily is true that an opening bid at Contract shows at least five probable tricks and that a contract of two-odd probably can be fulfilled in case declarer's partner holds even three assisting tricks, but that does not mean that sound strategy is to assist upon less than average strength, as the declarer counts upon finding three tricks in dummy. An opening one-bid may show either 4, 5, or 6 tricks, but a stronger hand calls for an opening bid of two-odd. The required tricks to go game from a love score cannot be made on a one-bid hand unless the bidder's partner holds at least 4 assisting tricks. As an opening bid of oneodd offers no game chances to a partner having only 3 tricks, he should not increase the contract; if two or three are made on an uncontested declaration the premium of 50 or Ioo points will be welcome. On the other hand an immediate assist of a 6-trick hand on 4 helping tricks, enables the declarer to jump to ASSISTING PARTNER I07 4-odd. Nothing can be lost by refusing to at once assist a dealer's opening bid of one-odd when something over 3 tricks is not held: If the dealer has an opportunity to rebid, he can be aided upon 3 tricks; if you decline to assist when you have nothing above 3 tricks, your partner may safely rebid a 5-trick hand that you have at once assisted, allowing you to again raise him if you also hold a 5-trick hand. The habit of jumping partner's opening declaration to 3-odd, because you hold just 5 assisting tricks, is a dangerous habit to form, as it indicates slam possibilities and should never be employed unless 3-odd means game or unless you expect that a slam may be made. Assisting partner once, instead of jumping the bid as was done frequently at Auction, is sufficient encouragement for him to rebid a 5-trick hand, or to show you a second suit that may better fit your own holdings, possibly allowing your side to collect a premium for overtricks or even to safely venture a slam. The same partner who wants you to raise him on a bare 3 tricks is frequently the chap who loses game by not rebidding his own 5-trick hand, after you have once aided him, thus not allowing you to raise him to a game contract. Such bidding is a relic of Auctionnot a feature of modern Contract. Another antique is referring to the strength of hands in terms of sure tricks instead of speaking of probable tricks or probable assisting tricks. Card distributions, minor honors held, and in dummy's case length of trumps and ability to ruff, are important features lost sight of by telling merely how io8 CORRECT CONTRACT BRIDGE many aces and kings are held. The two following hands possess equal sure trick strength, but there is a difference in favor of the first hand of I 2 probable tricks: 4 AK o7 v A6 * AJ4 0 J o 6 3 * AK87 v A6 4 A54 0 7632 It is not customary to open the bidding, third or fourth hand, upon less than a 6-trick hand, so that such an opening declaration invites and expects an assist upon a bare 3 tricks, allowing its bidder to recall his make if aided, to see whether or not you can again raise his declaration in case he cannot at once bid for game; as, after you have once passed your opportunity to open the contracting, your partner does not often hold cards which he expects can make a slam. Because you have once passed, your partner's opening bid, even fourth hand, may denote as much as 7 tricks in a major suit or 8 tricks in a minor make, without causing him to open with a bid of two-odd. Certainly he is not opening the bidding so late in the contracting on any holding asking much of any support for fulfillment of his contract, or expecting more than average assistance or a bit better, to go game, or to help you go game at your best make in case he opens with a minor bid. RECTIFYING DUMMY S TRUMP VALUES Chapter IV, under "Valuing Dummy's Trumps," shows how to value all trump holdings of dummy except the more complex cases where credits must be ASSISTING PARTNER lo9 allowed for honors held and where at the same time deductions must be made for shortage of the number of trumps held. The following illustrations will make clear the method employed to rectify dummy's trump holdings of honors, when fewer than three trumps are held. The ace of trumps is worth I Y2 tricks in dummy, as well as when held by the declarer. If dummy holds just A X X the value is i 2 trump tricks; in case dummy holds A X X X the value is 2 tricks, I 2 tricks for the ace and the added /2 trick for four trumps. In case only the A X are held the ace is still worth i Y2 tricks but holding one trump fewer than three deducts Y2 trick, so that the final value assigned to A X is only one trump trick. In case the singleton ace of trumps is in dummy the rectified value is i 2 less I trick, because dummy is short two trumps of normal support, a final value of Y2 trick, or Y2 trick better on an average than having three worthless trumps and neither declarer nor dummy holding the ace. Calculating in similar manner, K X X = I trick; K X = - 2 == 2 tricks; K only, the precise equivalent of three small trumps. Q X X = 4 tricks; Q X - Y4 trick; Q only, minus Y4 trick, or poorer than three small trumps. Thus either the lone ace or king, or the singly guarded Q, affords normal trump support, just the equivalent of three small trumps, but the singleton Q does not afford normal trump support. The J X X X has a value of one full assisting trick, 2 trick for the fully guarded J, plus ~2 trick for four trumps. The "1o CORRECT CONTRACT BRIDGE J X X has only a value of Y4 trump trick, because its shortage of one needed guard reduces the normal value of Yz trick by Y4 trick. The Io X X X has a value of M4 trick but the 10 X X possesses no appreciable value beyond that of three lesser trumps. No trouble will be experienced in valuing any honor combination if you will first calculate the value that the combination possesses as part of a side suit; to this add the value of 4 trumps or 5 trumps, if held; or if fewer than three trumps are held you deduct 2 trick for a shortage of one trump in case just two honors are held. For example: the K Io X X are worth Ij4 tricks; the K Io X are worth only I 4 tricks; the K io have a value of just y4 trick. XIII REBIDDING A FIRST bid rarely discloses the full strength of a hand, but in Contract it is poor strategy to rebid against a declaration incapable of scoring game or slam, unless you either can score game or slam, or unless you are certain to collect a penalty from further adverse contracting. Assuming that an adverse declaration cannot score game, your rebid announces two facts: the possession of greater values than shown by your previous bid; a strong hope that you may go game. Before rebidding, ask yourself: "How many tricks have I already stated that I can win?" Efficient rules for contracting and the meaning to be attached to each bid should be based upon chances for success, rather than upon mere personal opinion. Keep clearly in mind the precise minimum number of tricks announced by each original declaration and the added number of tricks shown by each assist and each rebid. For examples of the above: An opening bid of I-Spade definitely announces that 4 tricks can be won by its bidder (It is almost certain that either 5 or 6 tricks can be won; it is unlikely that the declarer can win 7 tricks, or he probably would have made a higher opening bid). An opening bid of I-Spade III 112 CORRECT CONTRACT BRIDGE cannot be expected to go game from a love score unless the declarer's partner can win at least 4 tricks, making it both useless and misleading for an assist to be made upon less than normal trump support and 4 probable tricks. In case the opening bidder knows that he will not be aided upon fewer than 4 tricks, he can raise his assisted declaration to 3-Spades in case he holds a bare 5 tricks, allowing his partner to end the contracting with 4-Spades if 5 assisting tricks are held, or expecting his partner to pass the 3-Spades in case the first assist has exhausted his resources. If the opening bidder has a 6-trick hand he will at once jump his partner's raise to 4-Spades. In case the assisting hand contains a minimum of 6 tricks, its holder should jump the bid to 3-Spades, to show game expectations and slam possibilities; this "slam signal" will be explained in detail later on, but here we may say that it demands that the original bidder "show" his lowest side ace, by bidding 4-odd in its suit, instead of saying 4-Spades; in case the declarer holds no side ace he must signify that lack by terminating the contracting with 4-Spades. If bidders adhere to sound and logical procedure the entire process of contracting is simple and will in the long run produce maximum scores. Unless made unnecessarily high, to show surplus strength, forced or secondary bids require partner to hold 4 tricks to raise. A third hand or fourth hand opening bid of ISpade discloses greater strength than a similar bid made by dealer or second hand, and upon that show REBIDDING II3 ing requires only 3 tricks to assist. It is declarer's business to realize that his partner's assist shows only 3 tricks and to govern his subsequent contracting accordingly. An immediate assist justifies the declarer's advance of his contract one trick for each trick that he holds in excess of what his first declaration announced. The following hands illustrate the rebidding of hands probably incapable of making slams. You open the contracting with I-Heart; your partner bids 2-Hearts over an adverse declaration of 2-Diamonds; you should bid 4-Hearts, as game seems probable: 4 AJ 5 3 v KQ9742 4 J I9 0 - You bid 2-Clubs over dealer's declaration of iSpade; your partner goes 3-Clubs over opponent's 2-Spades; you may advance your contract to 4 -Clubs: * 52 v A83 * AKQ 6 0 97 5 Your opening make of i-Diamond is raised by your partner to 2-Diamonds over an adverse iSpade; unless opponents have an advanced score you should not rebid, whether your opponents pass or bid 2-Spades; you have better chances to save game than you have to go game: io 6 V A932 4 84 0 AK I-53 II4 CORRECT CONTRACT BRIDGE UNASSISTED REB IDS An unaided rebid shows 2 more tricks than your previous declaration (One trick more than originally shown is needed to increase your declaration and the second trick more than already announced is required to supply the one trick that your partner's failure to assist shows that he lacks). Whether your partner's failure to aid your declaration was due to lack of 4 helping tricks or to lack of normal trump support, your rebid justifies his assist on either normal trump support and 3 tricks, or upon 4 assisting tricks although he holds only two small trumps. Application of the "Rule of Five" will enable your partner to judge how high you must bid before he can properly assist. Ordinarily a preemptive declaration shows the full strength of your hand, requiring an assist from partner before you can rebid (Unless you deliberately overbid to save game), but sometimes even a preemptive bid may not fully disclose the strength held, as detailed below. In general a preemptive declaration expects partner to win two tricks for fulfillment of the contract, and invites an assist in case partner holds at least three probable tricks (Which three tricks are slightly more than an average hand can supply a partner bidding a freak hand that requires specific cards to help, although three tricks can ordinarily be supplied as aid for a declaration on a normal hand, more evenly divided among the suits). A few excellent players will not bid game pre REBIDDING II5 emptively unless they can see all needed tricks in their own hands. Possibly their object may be to enable their partners to safely bid slams in case such extra tricks are held by partners. But slams are infrequent with hands calling for preemptive bids-even more rare than common. In the meanwhile games may be sacrificed just because bidders will not rely upon the probability of finding two assisting tricks in dummy and allowing them to assist in case three probable tricks are held. Under this more elastic system of contracting you may bid 4-Hearts upon a hand unsuited for an opening bid of 2-Hearts, whether your hand has 8, 9, or 10 tricks total. If another ventures to overcall your 4-Hearts with 4-Spades or 5-odd in a minor suit you should not make an unaided rebid of either an 8-trick or a 9-trick hand; your partner will assist you in case he can win 3 tricks; he will assist you on ability to win 2 tricks in case he deems game in danger of going to opponents. But if you happen to have 10 tricks in your own hand you must signify this fact by making an unaided rebid of 5 -Hearts (Or by doubling in case you prefer a profit from an obvious overbid), to show 2 tricks held more than the minimum required for your opening bid. Upon receipt of this news your partner will take such action as his hand calls for. To illustrate how slender support of the right kind will sometimes give a declarer game, look at the following hand, upon which I made an opening bid of 5-Clubs, because I held 9 countable tricks (Or to be more precise, because my hand counted ii6 CORRECT CONTRACT BRIDGE 9/4 probable tricks), within 2 tricks of game, and because I had a right to expect 2 tricks from my partner. * 8 v AK9 * AQJ io6432 0 6 My partner held no face card except the missing v Q, but this gave me one entry to his hand, affording me an opportunity to lead and finesse my trumps, enabling me to capture the once guarded king of trumps at my right. Of course the thing turned out remarkably well, but had I not opened with a game bid I certainly would not have been raised by my partner, nor would I have scored game. XIV BUSINESS DOUBLES A DOUBLE means "business" (That the contract can be defeated): if not made at the first opportunity afforded to double any declaration; or if the contract doubled is either 2-No Trumps, 4 -odd in a major suit or 5-odd in a minor suit (Or any lower bid agreed upon with partner). The majority of players are not sufficiently quick about doubling, allowing more than half their defeats of opposing bids to be undoubled. Unless you fail to defeat about one in four or five contracts that you double, you may rest assured that you do not double often enough. Being quick to double overbids slows up adverse contracting, but you cannot expect to defeat every contract that you double. A "free double" occurs when a game contract has been undertaken. A "forced double" is one made of a contract for less than game. You may make a free double upon probable ability to defeat the declarer a single trick, but you should not attempt a forced double unless expecting to defeat the contract at least two tricks. Frequently a double costs its maker a trick through enabling the declarer to finesse through located strength. So many close doubles fail to penalize that you should not shift your partner's make 117 ii8 CORRECT CONTRACT BRIDGE merely because he has been doubled; only shift partner's doubled make when you would have done so or could reasonably have done so had he not been doubled. It rarely pays to double a declaration that you can defeat unless you are equally able to double any shift of make. Unless a business double will probably yield more than going game, either help your partner once before doubling or first try a shift to a strong declaration. OVERCALLING PARTNERS DOUBLE There are two sound reasons for overcalling your partner's business double: the first is probable ability to win game for a greater score than will result from defeating the opposing contract; the second reason is having misled your partner as to your defensive strength. If, for example, you have taken your partner out of i-No Trump with 3 -Hearts, on the hand shown below, you should bid 4-Hearts in case your partner doubles 3-Spades or 4-Clubs, as your partner will probably expect to find at least one defensive trick in your hand: * 74 OX QJ Io85432 * - 0 965 RELATIVE VALUES OF GAMES AND PENALTIES When able to choose between a definite penalty and a sure game, proceed as follows: Score, Love-All (o-o): Take 6oo00 points penalty BUSINESS DOUBLES II9 in preference to game; risk a possible overbid of three tricks to save game; Game-In: Take 600 points penalty in place of game; risk an overbid of only one trick to prevent opponents from tying the score; Game-Out: Overbid three tricks to save the second game; accept 600 points in lieu of tying the score; Rubber Game: Overbid one trick to save rubber; accept 00oo points in place of rubber game. What follows need not be read unless you are interested in discovering how the above rules are obtained. Judging from what has been written concerning the relative values of Contract games and penalties, it seems that shifting from the arithmetical progression of Auction penalties to the pseudo-geometrical progression of Contract penalties has sadly befogged players. The way that the premiums are awarded for winning games and rubber also confuse calculators of relative values. The winner of each game receives 200 points premium and the winner of the rubber is awarded 300 points additional premium (The winner of a love rubber receives 200 for his first game, plus 200 for his second game, plus 300 points for his third game, or 700 points total. The winner of 2 out of 3 games receives 200 points for his first game, plus 200 points for his second game, plus 300 points for the rubber, minus 200 points because his opponents have won a game, or 500 points total). The direct results of winning the first game are 120 CORRECT CONTRACT BRIDGE scoring Ioo points won in tricks, plus a credit of 200 points premium, to be adjusted when rubber is scored, or a total of 300 points made through winning that first game. Also winning that first game gives an equity of 450 points in the rubber (This consists of y4 x 600), leaving the losers of the first game an equity in the rubber of only 150 points. Overtricks, honors held, and slams negotiated are termed "hazards," as no account of them can be made when calculating whether overbidding is preferable to surrendering a certain game. The average amount that a side can afford to overbid to save any particular game may be calculated as given below. Suppose on four occasions that you overbid to save the first game of the rubber. You will average to win half the four rubbers, and on a long series of such happenings you will finally lose precisely what it cost you in overbids to save those first games. Now suppose that instead of overbidding to save those four first games you allow the other side to win each of them, giving that side a score of 4 x 300 = I200 points. You will win two of the four second games, giving you a score of 600 points. You will also win one of the four rubbers, giving you an added score of 600 points. Your total score will be 1200 points. The other side will win three of the four rubbers, scoring for their second game on each 600 points, or 80oo points for second games won. The other side will have made a total score of 3000 points on the rubbers that they won, or a total of I8oo points net gain on the four rubbers BUSINESS DOUBLES 12I that you failed to contest. If your overbids to save the first games of those other four rubbers did not cost you i8oo points, your overbids saved points for you, and in general you will find that any overbid costing you less than 500 points to save the first game of a rubber will save you something. An overbid of 3 tricks doubled will cost you 400 points, which is a justifiable loss. An overbid of 4 tricks doubled will cost you 600 points, which is not justified. On his side, the player able to win a certain first game cannot afford to accept less than 600 points to let you play the hand. Next, suppose that on four occasions when you are a game behind you overbid to save a certain game that opponents can win. They are already I200 points ahead; you will win the second game of two of those four cases, giving you a credit of 600 points. You will lose the second game of two of the four, costing you in each instance 600 points, or I200 points total. You will win the third game of one of the two rubbers whereof you won the second game, crediting you 600 points; you will lose the third game of the other rubber, costing you 600 points. The opponents make a net score of 800o points. Had you not overbid your opponents would have won all four rubbers, winning 3600 points. Anything that your overbids cost you less than I8oo points was a gain for you. As on the first games, you could afford to overbid 3 tricks doubled, costing you 400 points each time, but the adversary with certain second games could not afford to let you play the hand unless you overbid 4 122 CORRECT CONTRACT BRIDGE tricks, costing you 6oo points to save the second game. Next, suppose four cases where your adversary is a game ahead and you are certain to win the second game unless he overbids; how much can he overbid, be doubled, and still make it pay? If he does not oppose you, half of the rubbers will go to each side, with a theoretically balanced score as a result. In case he overbids to save letting you win a certain second game, he will end by winning two rubbers with net scores of 9oo points each, or i 8oo points for the two. He will win a third rubber in which you have won a single game, giving him a net score of 6oo points, or 2400 points total for his three rubbers won. You will win the fourth rubber with a net total score of 6oo points, giving him a net gain on the four rubbers of i 8oo points. As an overbid of two tricks, doubled when vulnerable, would cost him 6oo points, the winner of the first game of a rubber cannot afford to overbid his hand more than a single trick to save a sure game. Last, suppose that on four occasions you are on the rubber game, and that your opponent is certain to win each rubber unless you overbid. How much dare you overbid? Those rubbers are each worth 6oo points if you refuse to overbid, or 2400 points total. If you dare overbid you will win half of the rubbers, giving a final score amounting only to the total that you have overbid. You cannot gain anything by a doubled overbid of 2 tricks, worth 6oo points, as you will be penalized 2400 points total on the four rubbers and you will end by win BUSINESS DOUBLES I23' ning only two 600 point rubbers to offset his two 600 point rubbers. You will save by being doubled on an overbid of a single trick per rubber, as then your net loss on the whole four rubbers will amount only to 800 points, a saving of 1600 points over let. ting your opponent walk off with 4 uncontested rub. bers. Your opponent will make no average gain by setting you 600 points on a rubber game that he can win. OVERBIDDING TO SAVE SLAMS Especially when you are a game behind, sometimes you may overbid heavily to save an evident slam. The following hand illustrates just such an incident: 7 qV Q9643 4 AKQJ io 0 KQ 4 8 4 Y KQJIo 96532 V 82 - * 97654 A B 82 0 7432 Z 098 A v A K J 10 7 5 4 2 0 AJ o 6 5 Our opponents (Y-Z) were vulnerable, but we had won no game. The bidding went: Z, 2-Hearts; A, pass; Y, 3-Hearts; I bid 3-Spades; Z, 4-Spades; 124 CORRECT CONTRACT BRIDGE A, pass; Y, 5-Clubs; I, 5-Spades; Z, 6-Diamonds; A, pass; Y, 7-Hearts; feeling almost certain that a grand slam would be made unless I outbid them, I went 7-Spades, knowing that I must go down five tricks doubled, or Iooo points less my Ioo honors. But a grand slam by my vulnerable opponents meant I5oo points as a starter. Even if they went rubber on the next deal I would save the slam premium, unless the unexpected happening of two slam hands running occurred. As we saved 300 points by winning the next game, when Y-Z won the rubber two games later, without honors or extra tricks, my overbid was found to have saved us just I290 points. SURE TRICKS SHOWN BY PARTNER'S BIDS In 1923 I published the first list offered of defensive tricks shown by partner's acts at Auction Bridge. We are now playing Contract Bridge and we also have discovered that contracting should be based more upon tricks total than upon the number of sure tricks held. On those two accounts the following list gives about the maximum defensive tricks that we have a right to consider in our partner's hand on account of what he has bid, before we make a business double of an adverse contract. Sure Tricks-Shown 2 An opening bid as dealer or second hand 3 An opening bid as third or fourth hand 3 An opening 2-bid 1X2 A preemptive opening bid BUSINESS DOUBLES 125 I A forced bid 2 An informatory double of i-odd 3 An informatory double of a bid higher than I-odd 3 A subsequent double 3 An assisting double of a suit make 3 An informatory double of each of two suits I A voluntary response made to a double, over an intervening bid I An unnecessarily high response to an informatory double Y2 A jumped assist o Secondary bids or normal responses to informatory doubles. xv GOULASHES SLIGHTLY differing in details and known by various local names, "Goulashes" appeared in Auction Bridge sometime before Contract Bridge was played in this country, but these unusual deals never became popular until the advent of the newer game. Commonly regarded only as a novelty, their real purpose was to break the monotony of a series of dull hands by insuring unusual distributions of cards. G OU L A S H E S (Optional) "Laws Of Contract Bridge," Copyright, I927, by The Whist Club, New York. "When all four players pass, no bid having been made, and the players desire to play a Goulash, the cards shall be redealt by the same dealer. Before surrendering his hand, each player shall sort his cards into suits, arranging the cards in each suit according to value (Law 3). The dealer then places his cards face down on the table, and each player in turn, beginning with the player on the right of the dealer, places his cards face down on top of those of the preceding player. The cards are then cut by the player at dealer's right (no shuffling of any 126 GOULASH ES I27 kind permitted) and are dealt as follows: Five at a time to each player in turn, beginning with the player on the left of the dealer, again five at a time to each player, and finally three at a time to each player." "When all four players pass, no bid having been made, the same procedure is followed as before, the cards being dealt by the same dealer." "If a misdeal is properly called the goulash is abandoned and the next dealer deals in the regular way with the still pack." COMMENTS ON GOULASH LAWS Appreciating the real object of an apparently childish proceeding, and enjoying the unusual character of "goulash" hands, experienced Contract players almost invariably insist upon these deals of passed-out hands. Of course "goulashes" cannot be played if even one of the four players refuses to participate in them. Equally, of course, the refusal of one player to continue unless "goulashes" are played terminates a game; one refusal is as reasonable as the other. Where players are divided in wishes concerning playing "goulashes" I always suggest that the last player to pass may say: "No bid, goulash," or he may say: "Pass, goulash." Only in this way will each player have his fair share of control of the debated deals. The Laws require cards of each suit to be arranged in order of value (A, K, Q, etc.), but the order in which the four suits shall be placed is not specified. Most players follow the natural custom 128 CORRECT CONTRACT BRIDGE of alternating the red and black suits, which is one of the best safeguards against revoking and which is the most courteous method of boarding dummy. Goulash deals are made from left to right, as are other deals, but the cards for a goulash deal are stacked by the players in the reverse order. No limit is prescribed for the number of successive goulash deals, although some clubs regulate the number by house rules. There is no authority for the use of "Philadelphia Goulashes" or for the "Push Four," where cards are exchanged by players after the deal. Each goulash is dealt in the 55-3 fashion. A petty crook sitting at the declarer's right can readily arrange his best cards so that his carefully calculated cut will insure them going to his partner. To obviate such dishonesty some players have suggested that each of the three non-dealing players cut the cards in rotation. Anyone with a little practise can master the pitiful art of determining to which player must have gone the remainder of his original sequence of a suit, when a part of that sequence appears in his hand on a redeal. Of course the ideal way of preventing cheating is to decline to play with those who may do something crooked. GOULASH BIDDING Ordinary deals cause the four cards of previous tricks to be evenly distributed in rotation to the four players, especially when the pack is insufficiently shuffled, making dull bidding. Because each GOULASH ES I29 player arranges all the cards of a suit in sequence before a goulash deal, of necessity many more long suits are held in goulashes than in regulation hands, which causes more spirited bidding and keener interest. A considerable proportion of goulashes divide an entire suit between two players. With two opponents and a single partner the balance of your 6, 7, or 8 trumps often gives one opponent 7, 6 or 5 trumps, respectively. Think of this possibility before you open the bidding on a suit lacking nearly solid tops or very great side strength, especially in case your partner has already passed, but his opening bid justifies a declaration by you upon moderate strength. It is not uncommon for an adversary to ruff an opening lead of one of your good side suits. There may even be established a cross-ruff of two of your side suits. I have known instances where a contractor failed to fulfill a grand slam contract, although he held the eleven top trumps with a side A-K; in each case the opening lead of his side suit was trumped. The added chances of having your side honors trumped make it somewhat hazardous to contract for the extreme number of visible tricks held. On the other hand, a player must use great dis. cretion in assuming ability to defeat a high contract upon side strength, unless opponents are obviously short of each other's suits. If your partner shows great length in his suit you must be careful not to count upon him for any help in defeating opponents. 130 CORRECT CONTRACT BRIDGE The following hand and the contracting are as freakish as often occur: 95 v 86 4 Q9876542 0 6 7 Y 4 A V — v AKQJ Io J Io A B 75432 0 AKQJ8 Z 4 A 75432 0 9 4 KQJ Io86432 9 4 K3 0 Io The contracting of the above hand went as follows: Z, pass; A, 5-Diamonds; Y, pass; B, 6 -Hearts; Z, 6-Spades; A, pass; Y, pass; B, 7-Hearts; Z, 7-Spades; A, pass; Y, pass; B, 7-No Trumps, which of course he made. As a rule goulashes favor suit makes but some deals afford perfectly sound no-trump opening bids. On several occasions I have found the following convention very helpful when partner opens with a bid of I-No Trump, but only on goulashes. By agreement with partner you must twice take him out of his no-trump, as he must hold strong help for one or the other of your long suits. In case you hold only a single long suit you must twice call it. With this convention in force your partner possibly may bid i-No Trump upon a real two-suiter. After GOULASH ES I3I his second return to no-trump he really asks you to choose between the two suits that you have not been able to bid. The following illustrative goulash deals show how well this convention sometimes works out, THE DOUBLE TAK E-O U T 952 v Q io8 2 4 Q J I0 7 6 0 6 A AQJ3 Y io 874 ' AK976 A 3 v AK2 9A B 853 O K 0 Q9872 K6 ' J54 94 0 AJ Io543 Contracting went on the above hand! Z, pass; A, i-No Trump; Y, pass; using the "double take-out," B bid 2-Diamonds; Z, pass; A, 2-No Trumps; Y, pass; B, 3-Spades; Z, pass; A, 4-Spades. A won two top club and two top heart tricks; B ruffed one heart and one club trick, and then went game by winning four spade tricks. Game cannot be won either at no-trump or at hearts. 132 CORRECT CONTRACT BRIDGE IO 6 5 3 * Q Io 7 5 0 Q9 7 3 2 74 Y * KJ Io83 v KQ987 A B J42 ~ 3 &D 86 0 AJio86 Z 0 K54 4 AQ9652 V A 4, AKJ942 0 -Without the double take-out convention the above hand must be bid spades; wise opponents will be in no rush to disturb that make and the hand will not go game. As the hand was actually contracted under the convention, game was made at clubs. Contracting went: Z, I-No Trump; A, pass; Y, 2-Diamonds; B, pass; Z, 2-No Trumps; A, pass; Y, 3 -Hearts; B, pass; Z, 3-No Trumps; A, pass; Y, 4 -Clubs; B, pass; Z, 5-Clubs. The convention is as yet not widely known, and it should be explained to opponents-no secret codes are allowed. The reason that the convention must not be attempted except at goulashes is because only those deals average to insure a long suit and bad side distributions in partner's hand, with strong chances that an adversary holds as many as the declarer of his longest suit. Opportunities to employ the convention are rare and its success demands that the no-trump bidder GOULASHES 133 hold at least five sure tricks in case his longest suit consists of only five cards with no second suit of more than four cards. The possession of two suits, each containing five or more cards, makes the safe minimum strength 4/2 sure tricks. Contrary to custom with normal deals, an opening lead of a suit with solid tops against a goulash declaration had best be the ace, instead of the king, or your partner may ruff your honor, thinking that you will lose the trick. THE INTERLUDE For the benefit of those who want reasons for procedure and proofs of statements made, several chapters on special topics are presented as an "interlude" between the subjects of Goulashes and Slam Bidding. These technical chapters need not be studied by readers desiring only rules of proper procedure. Up to date I have both studied and taught eight systems of contracting, differing from others in certain vital features, abandoning one as soon as another better system was discovered. I have neither prejudice nor preference until scientific analyses and practical results unite in obliging me to choose between alternatives. Not infrequently, widely advertised suggestions and procedure especially favored by famous players who have become accustomed to their favorites' limitations, are really inferior to newer or less well known methods. As remarked before, highly trained players instinctively rectify the failings of poor methods of procedure, sometimes to a point that the players are unconscious of those weaknesses, but less well drilled players cannot afford to accept anything except the best methods. 134 XVI AVERAGES AND PROBABILITIES NE reason for prevalent erroneous theories offered Contract students is because nearly all writers and teachers who refer to the mathematics of Bridge fail to distinguish between averages and probabilities. An average is an arithmetical mean, while a probability is the likelihood of the occurrence of any particular form of an event; these two may differ widely. Suppose, for example, that you hold just 4 cards of a suit; on an average each of the three remaining players will hold 3 cards, but in a particular instance there are only about i i in ioo chances that the remaining 9 cards of your suit will be distributed among the other players 3-3-3. Again, suppose that you and dummy have between you 7 cards of a suit; you may say that on an average each other player will hold 3 cards, but the probabilities are about 65 chances in ioo against this happening on a particular hand. Sometimes it is a very simple matter to determine a probability; at times the calculation of probable chances involve methods unknown to the majority of players. For example, any student provided with a table of card distributions may inform you that 13 cards of a suit average to appear in i58, 753,389,900 deals. If such an event has just I35 136 CORRECT CONTRACT BRIDGE taken place the probability of its rehappening is obtained from the following rule: When the chances for an event to occur are extremely small, after the event has happened, we obtain the probable time of its next occurrence by multiplying the average interval of its appearance by the hyperbolic or Naperian log. of 2 (0.69314 -71865599, etc.). To obtain an approximate idea of the probable number of deals to obtain 13 cards of some suit in one hand we have: I58,753,389,900 x 0.693I5 = I10,039,912,209 deals. Without attempting to teach the mathematics of the game, the above illustrations will show that the man depending solely upon a limited knowledge of averages will often be deceived concerning probable happenings. CARD DISTRIB UTIONS 4 4 3 2 216 times 6 5 1 I 7 -5 5 3 2 155 " 6520 6 543 I 129 7222 5 5422 I06 " 74 1 4 4 3 33 I05 7 4 2 0 3 6 3 2 2 57 7 3 3 2 6 4 2 I 47 8 2 2 2 6 3 3 I 35 8 3 I I Itime 5 5 2 I 32 8 3 2 0 I 4 4 4 I 30 7 5 I I 732 I 9 I9 66 o I 6 4 3 o I3 " 8 4 I o I 5440 13 5530 9 "Total 1,000 AVE RAG ES I37 The foregoing table gives the 26 most common distributions of the 39 possible ways that a suit may be held, the remaining 13 ways each occur fewer than once in one thousand times. The first five distributions tabulated occur 711 times in IOOO. No distribution happening less than 3 times in Iooo need be considered in practical work, as it cannot average to appear as frequently as once in Ioo deals, considering all four suits or all four players' hands. (Card distributions for the entire 635, 013,559,600 different hands possible to deal may be found in "Correct Auction," by E. V. Shepard, Harper & Brothers, 1920.) The table shows the number of times in Iooo deals that a specified player will average to find his 13 cards divided among the 4 suits in any particular manner. The table also shows the number of times in Iooo deals that a specified suit will have its 13 cards divided among the 4 players in a particular way. The number of times that a given player will hold any specified division of his I3 cards among the 4 suits always equals the number of times that any particular suit will be divided among the 4 players in like proportions, but there is no reason to expect that these two particular events will occur at the same time (For proof of these statements see "Auction Bridge Magazine," page Ioo, December, I927, "Proof of Statistics Demanded By Bridge Students," by E. V. Shepard). XVII LAWS OF SYMMETRY GENERATIONS ago Whist players noted certain coincidences of like holdings or distributions in two or more hands. A few simple truths and probably more fictions were the results. During the past decade sufficient study of the subject has resulted in proof of a number of facts (See "The Field," London, October i6 and 23, I924, "Symmetry of Hands," by E. V. Shepard, for the first mathematical proofs of the Theorems given below and the first Glossary). GLOSSARY OF SYMMETRY Universal use of standard terms simplifies a new subject and obviates any excuse for a later writer to coin new words to express one of these terms: Duplicated: A feature reproduced. Like divisions of two suits or two hands. Feature: A salient point of a holding or a card distribution. Horizontal Distribution: Division of a suit among the four players. Hypothesis: A conjecture. A statement offering an assumption without proof. Laws of Symmetry of Hands: Sum total of the known Theorems on Symmetry of Hands. I38 LAWS OF SYMMETRY I39 Limit of Symmetry: Rarest feature having better than even chances of duplication or parallelism, under prescribed conditions. Paralleled: A horizontal division of a specified suit matched by the vertical division of a player's hand, or vice versa. Similitude: Repetition of a card distribution or feature, through either duplication or parallelism. Symmetry: Correspondence of parts or elements. Symmetry of Hands: Simultaneous appearance of like distributions or a duplication in one hand of an element of another hand. Theorem: General statement capable of being proven. Type: One having or exemplifying characteristics common to a number; a model or standard. Vertical Distribution: Division between suits of a player's cards. LIMITS OF SYMMETRY Symmetry of hands is due to correspondence of parts or elements. The frequency with which any given feature averages to appear alone determines the chances for a like feature to appear in the same deal. Personal opinions, the results of limited tests, or mere coincidences, have no legitimate place in any discussion of the subject; mathematical laws govern the whole subject of symmetry. There is a fixed minimum limit for the number of times which a feature must average to appear, for it to more than half the time have a similitude. 140 CORRECT CONTRACT BRIDGE An event averaging to occur only 20 times in 100 opportunities, if capable of duplication by a maximum of three suits or three hands, will be duplicated only 488,oo000 times in 1,000,000 cases, and unduplicated 512,000 times Evidently an event must appear more frequently than 20 times in 100 to expect its duplication when discovered in your own hand. An event averaging to occur 21 times in 100 opportunities, if capable of being duplicated by any or all of three hands (or suits) will be duplicated by at least one of those hands (or suits), 506,961, and unduplicatec 493,039, times in i,000,000 opportunities. Thus we establish as our minimum limit for an event to probably be duplicated by at least one of three possibilities, that such an event must average to appear 21 times in ioo00 opportunities. This proven fact gives us the first of the three Theorems that follow. There are only three chances for duplication, because one of the four hands or four suits contains the original. But a feature of a vertical distribution may be paralleled by a horizontal distribution of any one of the four suits, permitting a lower limit of symmetry for parallelism than for duplication. An event or feature that has i6 in ioo00 chances to appear, results in being paralleled 50,212,864 times in 100,000,000 opportunities, and being unparalleled 49,787,136 times; thus establishing the limit of symmetry for parallelism-giving us Theorem 2. LAWS OF SYMMETRY l4I There are 7 chances for a feature to have at least one similitude: 3 chances through duplication and 4 chances of being paralleled. Thus an event averaging to appear 8 times in o00 chances, causes it to be duplicated 22,I31,200 times, and paralleled 28,360,704 times, in I00,000,000 cases, or a total of 50,49I,904 similitudes to appear on an average in I00,000,000 opportunities. This gives us proof of our third and last theorem. Theorem 1. A feature having not fewer than 2I in 1oo chances to appear, averages to be duplicated, at least once, in any deal in which it appears. Theorem 2. A feature having not fewer than 16 in o00 chances to appear, averages to be paralleled, at least once, in any deal in which it appears. Theorem 3. A feature having not fewer than 8 in o00 chances to appear, averages to be either duplicated or paralleled, or both, at least once, in any deal in which it appears. PRACTICAL RESULTS The knowledge that such things as Laws of Symmetry really exist doubtless will afford theorists an added opportunity to make themselves heard, but practical players will derive little satisfaction from the subject. Turning back to our table of Card Distributions we find only a single one, the 4 4 3 2, that occurs nearly often enough to fulfill the requirements of Theorem I. The second most common distribution (5 3 3 2, 55, instead of I60 times in I,ooo) falls somewhat short of even meeting 142 CORRECT CONTRACT BRIDGE the lower requirements of Theorem 2. But all five of the most common distributions meet fully the very low requirements of Theorem 3. Unfortunately for all practical purposes, a player can have no idea in which one of the seven possible ways the similitude will appear. Will his vertical distribution be duplicated by partner, opponent at his right or by the one at his left? Or which one of the four suits will parallel his hand distribution? A singleton appears so frequently that the odds for its duplication are 657 to 343; such odds make it really worth while to anticipate that some other player will duplicate your singleton, perhaps in the most unexpected suit. Through the sum total of expected and unexpected similitudes you may expect to encounter at least one in nearly every deal made, but base your actions on known probabilities of card distributions, rather than pin your faith upon a guess concerning which of seven possible things may happen. XVIII UNNECESSARILY HIGH BIDS M ORE often in Contract than in Auction Bridge, unnecessarily high bids are made to convey special meanings to partner and to urge him, if reasonably possible, to make some responsive declaration. Needlessly high bids regularly employed by Contract players are listed below. I. Preemptive Bids. Just as in Auction, opening bids of 3-odd or 4-odd in major suits, or of 4-odd or 5-odd in minor suits, are employed to show hands unadapted to other declarations, needing two assisting tricks from partner for fulfillment of contract and asking him to assist contracts for less than game in case he can win three tricks. 2. Game Signal. Slams should seldom be attempted at no-trumps; an opening bid of 2-No Trumps signals game expectations, asking partner to do something if holding a single definite trick (an ace or its equivalent); the partner may either bid game at no-trump or he may show his best suit, as later explained. The naming of just a game contract by either partner, under any conditions of score, is "the stop signal," stating that game is the limit of probable ability. 3. Slam Signal. "Game expectations and slam I43 I44 CORRECT CONTRACT BRIDGE hopes" are signalled in various ways: by an opening bid of 2-odd; by jumping partner's opening bid of i-odd to 3-odd; by overcalling another's bid by one trick more than necessary; by bidding opponent's suit, instead of at once raising partner's make; if necessary to avoid naming just a game contract, by bidding a trick more than game. All the above bids are integral parts of Contract and each will be found more in detail in its appropriate place in this book. They require no new names or special featuring, but if you think that calling some of these needlessly high bids by newer names than "jumped bids," makes them more impressive, you may term them "demand bids," "obliging bids," or "forcing bids," without in the least changing their nature or intent. Players who are still playing Auction, by merely changing their scoring, whether they are "trick counting" or employing extreme "approach" methods or other features savoring of poker tactics, fiave other uses for unnecessarily high bids, but these special uses of such bids have nothing to do with the system of contracting outlined in this work. XIX FOUR-CARD BIDS ON an average 6 of the I3 tricks at a suit make are won by trumps; to have a bare even chance of finding his declaration satisfactory, the declarer must be able to win at least 3 trump tricks; only the 4-card suits given below meet these modest requirements: A K Q X 32 probable tricks;A K J X = 34; A K o X =3; A Q J X 3; K Q J Io= 3 probable tricks. In each instance sufficient side strength must be held to bring the value of the hand to at least 5 tricks. For each 4 trick that trumps fall short of averaging to be worth the full 3 tricks, add Y2 side trick to the 5 tricks ordinarily required, as illustrated below: 4 AK84 Iv KQ6 4 K73 0 952 4 AQ93 q7 4 AJ64 0 KJ75 With the above compensation for trump weakness, I consider that greater probability for success lies with an opening bid of I-Spade; with less than 145 146 CORRECT CONTRACT BRIDGE the above compensation for trump weakness I would favor an opening bid of I-No Trump on either hand, regardless of the low singleton in the last hand. The very precise minimums given throughout this work are intended as guides in the absence of something more tangible, such as may be observed in special cases. They are the least values that habitually followed give better than even chances for success. In any special instance such factors as the score, the relative ability of players, partner's reliability, or the way the cards have been running, may either urge you to temporarily increase your minimum requirements or justify action upon lesser holdings. Unless an able player is also a trained educator his advice or his example may be dangerous for less able players to accept as sound general practice. INHERENT WEAKNESS OF 4-CARD SUITS Each of the three suits shown below possesses the same average strength as trumps; no declarer would feel very proud of any one of them, and each needs considerable side strength to justify its use for an opening bid. Four-card bids are as old as Bridge, justifiable when discreetly employed but abominable as frequently used-at best they are frail supports upon which to place much reliance. AKIo7 A Io754 J I7543 FOUR CARD BIDS I47 In the first place, 59 in ioo times, at least one ad. versary will hold as many or more than your 4 trumps. To be "efficient" means that a suit need lose no trick to an adversary, either because the latter holds more trumps or because he has one honor trick. "The net efficiency" of a trump suit consists of its average chances to find normal support in dummy, minus the average chances of finding an opponent able to win at least one trump trick. Really the term "normal support," as scientifically used, means that the declarer and the dummy jointly hold 8 trumps (Whether divided between them 4-4, 5-3, 6-2, 7-I, or 8-o, does not matter; there are held against their side just 5 trumps, standing 68 in ioo chances of being divided 3-2), or 7 trumps, in case dummy holds a missing high honor. Sometimes a player having small regard for facts, states that the strongest possible arrangement of these 8 trumps is when declarer and dummy each holds four. Of course this is absurd; the A K Q X X X X X held by the declarer, with none in dummy averages to be worth 8 tricks, which is 3 more tricks than an average division is worth. Your chances to find normal trump support in dummy are, in I,000: 44I for a 4 card suit; 6I7 for a 5 card suit; 79I for a 6 card suit. Chances for an efficient trump suit are in I,000: 3I3 for a 4 card suit; 593 for a 5 card suit; 79I for a 6 card suit. With relative efficiencies of 3, 6, and 8 chances in IO, for 4, 5, and 6 card suits, respectively, it should be evident that when reasonably possible 4-card bids should be avoided. 148 CORRECT CONTRACT BRIDGE FIVE-CARD SUIT BIDS MOST FREQUENT Of all hands that can be dealt 66% contain a suit of at least 5 cards. As compared to s-card suits, suits of only 4 cards have 3/5 the chances to contain two specified honors; 2/5 the chances to have three honors; only 1/5 the chances to contain four honors (for proofs see The Auction Bridge Magazine, March, I928, page 237, by E. V. Shepard). The comparative rarity with which 4-card suits contain bidding strength affords small grounds for thinking, as some players do, that partner may be bidding a suit of only 4 cards and hence that they must not assist unless they also hold four cards of his suit. Within reasonable limits all players employ 4 -card bids. Only the extremes to which the radical goes should be condemned-employing the discredited "invitation bids" of a past generation, rather than bid perfectly sound no trumps, with one unguarded suit-relying upon mere hypotheses concerning "symmetry" or "hand patterns"-blindly groping for partner's best suit, instead of clearly revealing his own holdings. It is a mystery why some players who fear to bid no-trump, because one suit contains a lone deuce or 3-2, will readily bid that no-trump in case they hold something like the 4 3 2. Certainly the shorter they are of a suit the greater chances their partners have to effectively stop the run of that suit. It requires a chain of coincidences to make dangerous a FOUR CARD BIDS 149 singleton in the hand of a no.trump declarers senior must have dangerous length in that suit and open it; junior must not bid for a lead; the no-trump bidder's partner must not make any declaration; the partner must be unable to effectively stop the run of the dangerous suit; there must be simultaneous appearance of all four of these possible happenings to render dangerous the declarer's singleton. The chance for each event to happen is represented by a fraction. The product of those four fractions shows the chances of the declarer to suffer through his possession of a singleton. The worst pessimist will not be alarmed at the small risk involved, even if he chooses his own fractions. xx CONTRACTING POWERFUL HANDS THE conviction that Bridge is a genuine science increases rapidly, as talks and correspondence with scientists, mathematicians, and the members of faculties of leading universities proves. It behooves us to consider the game more from a scientific standpoint and less than has been done in the past from the personal viewpoint of prominent players, otherwise we cannot always rapidly progress in the right direction. TOPOGRAPHY OF CONTRACT A properly trained "contract engineer" utilizes bids as a topographer employs symbols, to describe in minute detail what he views in his hand. The definite values required for the probable success of certain declarations are announced by their holder in set terms, which are a feature of "slam bidding." As previously remarked, the custom of making an opening bid of two, to announce "game expectations and slam hopes," originated among Auction players, who unofficially allowed Soo points for a small slam and i,ooo points for a grand slam, when both bid and made. The sole use of the opening two bid of any suit was to notify partner of slam prospects; hence this bid was termed "the slam signal." This I50 POWERFUL HANDS I5i slam signal was also given by unnecessarily jumping partner's opening one bid to three, or by bidding a suit named by an adversary, to show strong support for partner's declaration and that no losing cards of the opposing suit were held. Slams were almost never attempted at no-trumps or on hands containing many high honors in short suits. It was natural for slam bidders of Auction to employ these tactics of proven efficiency when they took up Contract Bridge. Contrary to a common misconception of writers and teachers, aces are never shown unless one partner or the other has given the slam signal. Your partner's raise of your opening bid to only two, may decide you to show him your second choice of two nearly equivalent suits, to discover whether he may not be better able to support the second declaration. But in case your partner shows strong approbation of your first make, by jumping your bid of one to three, you have no occasion to offer him a choice of makes, so that your bid of a second suit shows that you hold its ace. Another error sometimes made by Auction players is to assume that slam bidding was devised as an aid for players who were unable to correctly value hands. All trained Contract players estimate the values of their hands, even more precisely than they were ever called upon to do at Auction. In reality it is more in accord with facts to say that slam bidding was evolved by those sufficiently versed in the mathematics of cards to realize that mere trick counting is too unreliable to justify slam at 152 CORRECT CONTRACT BRIDGE tempts without more specific information concerning how the joint 26 cards of a side fit. The chief object of slam bidding is to discover whether any suit contains losers, so as to confine contracting within the limits of safety. The first reaction of Auction players to contracting methods is to resent the radical departures from Auction procedure; their second thought is to attempt to improve upon "slam bidding," by recourse to methods more in accord with those of the older game. THE SHORT SUIT SYSTEM Slam bidding as transferred from Auction to Contract consisted almost entirely of attempts to safely achieve slams with long and almost solid trump suits, with sufficient side strength to warrant strong hopes of finding that the joint 26 cards held no losers. We will refer to this as "the long suit system." Short suits containing many high honors were utilized almost exclusively for no-trump makes. No hand containing less than seven probable tricks possesses the probability of going game. With "the short suit system" as an adjunct, an opening bid of two may be made on any 7 trick hand consisting of the following as a minimum: I. Six cards headed by A K Q, with a side ace or its equivalent; 2. Five cards headed by A K Q, with two definite side tricks; 3. Four cards headed by A K, with three sure side tricks in two suits. POWERFUL HANDS I53 Such holdings possess the probability of going game in case they can be played at spades or hearts, but an added trick is required to attain game probabilities at diamonds or clubs. Although the above holdings barely possess game probabilities, you need not be surprised to learn that players often advocate bidding two on smaller holdings; of course these lighter bids will fall below game probabilities and are suitable only for purposes of obtaining partial game scores and for emergencies. Either the long suit system or the short suit system requires partner to hold a minimum of a single definite trick (an ace or its equivalent K Q or two side kings) to raise an opening bid of two. The long suit system permits partner to assist although he holds only two small trumps but the short suit system requires partner to hold a minimum of four small trumps or three including one of the high honors. Of course an advocate of either long suit or short suit system will open with a two-bid on all long suits so employed by long suiters, so when an opening bid of two is made by a short suiter it is impossible to tell whether he holds a long suit or a short one. Not knowing the length of suit held, the opening bidder's partner must always assume that a short suit is being bid-a serious handicap in many instances. In case the opening bidder's partner lacks the prescribed trump strength for assisting 4-card suit declarations, if he has one definite trick he proceeds to declare any biddable suit; lacking a biddable suit, one definite trick calls for a bid of 3-No 154 CORRECT CONTRACT BRIDGE Trumps. In case the opening bidder's partner possesses the requisite trump strength he may pass, if he lacks a definite trick; having neither the required trump strength to pass nor the one definite trick to increase the contract, the opening bidder's partner must bid 2-No Trumps to show a "bust." Having overcalled the opening two-bid, for the first time is disclosed whether the original bid was made on a long suit or on one of only four cards, provided the overcall was anything except an assist. Whether the original bidder has a long or a short suit, he will at least carry an assist to game, provided he holds the values that his opening bid indicates. With a long suit he will rebid over a 2 -No Trumps, but in most cases he must pass that make on a 4-card suit. Unless he holds exceptional aid for a shift of suit make, the original bidder will recall his own make on a long suit. Going back to 4-odd will show a long suit when 3-No Trumps is the response to the opening two-bid. In rare cases the opening bidder may show a second suit, provided it is nearly as good as that of his opening make, over any shift of declaration. In case his partner shows probable game-going strength by making an unnecessarily high take-out, the original bidder must render possible assistance to the new call, unless having a certain game at his own declaration. The following deal that I recently noted in detail illustrates proper short suit procedure, when the opening bidder holds a minimum of 5 sure tricks, with one unguarded suit: POWERFUL HANDS I55 Q73 V Q6 KQ87 99765 A 9 8 Y A 0o 542 J Io 4 2 A B v 9753 * A IO 9 4 * J 6 5 0 KQJ Z O io4 A AKJ6 v AK8 * 32 0 A832 Of course Y knew in advance that Z's opening bid of 2-Spades might be made on a 4-card suit. Having unusual aid Y raised to 3-Spades. Having nothing of consequence beyond what he had already shown, Z ended the contracting with 4-Spades, losing two diamonds and one club, just fulfilling his contract. Let us assume that the holdings of A and Y had been interchanged, to note procedure. A would have bid 3-No Trumps; B would have led his lowest heart and game would have resulted. Next assume that the holdings of B and Y had been interchanged: having unusual aid for spades, without a definite side trick, the holdings of B would have caused Z's partner to pass the opening bid, which could readily have been fulfilled. If Z and B had been paired, had B held one less spade and one more diamond the 2-Spades must have been shifted to 2-No Trumps, under ordinary I56 CORRECT CONTRACT BRIDGE rules, but some players do not wish any action on a "bust." Of course Z would have to let a take-out of 2-No Trumps stand, regardless of what might happen. Provided partners understand the short suit system and adhere to the requirements of having 5 sure tricks as a minimum in tops, this method of contracting powerful hands containing no suit of more than 4 cards gives excellent results. Attempts to use this' system on hands weaker than specified ordinarily results in needless overbidding, except in cases where opening bids of one would have proven equally efficacious. THE NO-TRUMP SYSTEM There has been employed for a much longer time than the short suit system another system of contracting powerful hands consisting of short suits. From its chief characteristic of opening with 2-No Trumps, instead of two of its best suit, we may designate this system as "the no-trump system" or "the no-trump approach." Having proven the slight danger of bidding no-trump with one unguarded suit, both mathematically and practically, for some years I have never hesitated to open with a bid of 2-No Trumps, to show 'a minimum of 6 probable tricks lying in 4 guarded suits or 7 probable tricks lying in 3 well-guarded suits. The opening bidder's partner was expected to assist upon a single definite trick, upon 3 probable tricks distributed, or to take out on any suit justifying a strength take-out of an opening bid of i-No Trump. POWERFUL HANDS I57 In 1928 I introduced a feature that increased the safety of the system and rendered procedure more flexible, as described below: Pass partner's opening bid of I-No Trump, unless you have either a sound assist or a strong takeout, but if partner opens with 2-No Trumps proceed as follows: I. Bid three of any 5-card suit once stopped or any 4-card suit twice stopped, unless you hold honors in all four suits-then bid 3-No Trumps; 2. Lacking a biddable suit, assist the no-trump with an evenly divided hand, provided you hold a minimum of one sure trick or 3 probable tricks, otherwise pass. Complete details of this system will be found in Chapter XXV; the above sketch of the subject will answer our present purpose. The hand given below illustrates general procedure, affording some comparison between this and the short suit system. 852 q2 Q9 4 J6 0 Q95432 K K Io94 Y * 73 V K 8 7 3 2 A B v A J I 5 4 4 984 4& K 10 3 2 08 Z J6 4 AQJ6 <> 6 AQ75 0 AK Io7 158 CORRECT CONTRACT BRIDGE As a choice between "invitation bids," urging partner to make some response, if possible, Z chose the "no-trump approach" declaration of 2-No Trumps, in preference to bidding two in his short spade suit. As a matter of fact, this particular hand would have called for a response of 3-Diamonds by Y, regardless of which system Z had been following. As diamonds happened to be one of Z's best suits, Z bid 4-Diamonds, which Y carried to 5-Diamonds and Z passed, Y making just what he bid. Suppose that the cards of A and Y had been interchanged. Then over Z's opening bid of 2-No Trumps the response would have been 3-Hearts. To show that hearts was his weak suit, Z would reply with 3-Spades (a perfectly sound response, as Z holds 3 probable tricks in that suit), which Z's partner would have carried to 4-Spades, ending the contracting. Through favorable location of missing cards a little slam would be made at spades, although neither partner could predict such a happening. The same final result would have been arrived at under the short suit system, had Z been a follower. Last of all suppose that the original holdings of Y and B had been reversed. In response to Z's opening bid of 2-No Trumps, his partner would bid 3-Hearts, which Z would overcall with 3-Spades and which B would venture to shift to 4-Clubs and Z would carry it to 5-Clubs; this might result in a little slam being made. Under the short suit system the hand would doubtless be played at no-trump and go game. POWERFUL HANDS 159 COMPARISONS OF SYSTEMS The short suit approach and the no-trump approach ordinarily result in the same final declaration. Sometimes the difference in final results favors one system, sometimes the other system appears best in a particular instance; in that respect there appears to be little advantage for either method. The chief consideration is clarity of meaning of the partnership contracting. No bid must have two possible meanings, unless absolutely unavoidable. Either an opening bid of two of a suit must mean: (i ) Partner, I have cards worth a probable game and a possible slam, with trumps probably incapable of losing more than one trump trick; you may assist me without particular regard to the number of trumps held in case you have one definite trick; or such an opening bid must mean, I hold high honors in three suits but hesitate to bid 2-No Trumps on account of one unguarded suit; if possible, indicate what your hand contains. With the majority of Contract players, contrary to the best practice at Auction Bridge, an opening bid of 2-No Trumps has always meant: I have a minimum of 6 probable tricks in four guarded suits or I have at least 7 tricks in three well-guarded suits. In addition it should mean: end the contracting with strength in three suits by going 3-No Trumps, or bid your best suit, provided it is a 4 -card suit twice stopped or a i-card suit containing a single stop; pass a trickless hand; bid 3-No I60 CORRECT CONTRACT BRIDGE Trumps on a sure trick in case you cannot bid your best suit. Evidently the no-trump approach is clearer in meaning than the short suit approach. The former states that either no-trump or a strong suit shift is the object of the opening declaration. The short suit approach method never states whether the declaration indicates a long trump suit or great strength held in honors of short suits; only subsequent procedure can clear that ambiguity of purpose. The no-trump approach wastes no time in arriving at an understanding between partners. The short suit approach often wastes at least one bid before the opening bidder's partner learns which type of holding caused the two-bid. A wasted bid or two when a slam is really sought often prevents one partner from showing some feature that will make plain to the other player whether or not game, little slam, or grand slam should be the limit of safe contracting. Before definitely deciding just what an opening bid of two of a suit should mean it will be best to consider the relative number of hands that meet the long suit requirements for probable games and slam possibilities, and the number of hands that contain the same number of probable tricks in high honors held in short suits. ANALYSIS OF OPENING TWO-BIDS In a complete series of all hands possible to deal, any designated suit (as hearts) will be distributed as follows: POWERFUL HANDS I6I 4 cards............ I5I,5I9,3 I9,38 times 5 "......... 79, 18,063,676 6 "........ 26,393,687,892 " Shorter suits cannot be bid, while suits of more than 6 cards ordinarily call for preemptive bids. For our immediate purpose we may confine ourselves to the consideration of suits of varying lengths, headed by A K or A K Q for 4-card suits, and headed by A K Q for 5-card and 6-card suits. For the needed side strength we will confine our remarks to those having side aces and kings, to which reference will be made when we speak of side tricks. A typical A K X X, with a side A K and another A, has an average value of 6 4 probable tricks, with its long suit as trumps; it also has an average assisting value of 652 probable tricks at partner's best make, or in case no-trump is declared. The hand is a trifle below proper minimum strength either for an opening bid of 2-Hearts or 2-No Trumps. Both the following hands are just f4 probable trick stronger than the above holding when played at hearts: A K Q X X, with a side A K; A K Q X X X, with a side A. But the three holdings are sufficiently alike in strength to justify comparisons, while unconsidered lesser honors held will constantly shift the strength in favor of one holding or another. Considering a specified suit only (Hearts) the following number of trumps will be held in a complete series of deals: 162 CORRECT CONTRACT BRIDGE A K X XorA K Q X 11,655,332,260 times A K Q X X 2,768,568,660 " A K Q XXX 1,845,7I2,440 " The three or four sure side tricks for 4-card suits must be confined to two suits, as honors in all four suits always makes no-trump preferable to a suit declaration. It is of no consequence how many guarded suits are held with a suit of either five or six cards, the general rule gives preference to the major suit declaration, when that suit is headed by A K Q. The following table recognizes these distinctions. A K Q K or A K X X, with 3 or 4 side tricks in only 2 suits.................-.....................404,657,880 times A K Q X or A K X X, with 3 or 4 side tricks in 3 suits.-........ —.4....-..........- 414,IIO,400 times A K Q X X, with 2 or more sure side tricks 509,723,280 times A K Q XX X, with I or more sure side tricks 934,342,200 times Slightly more than half the 4-card suits meeting all the specified requirements afford better opening bids of 2-No Trumps than 2-Hearts. When you add the number of fourth suits lacking aces and kings, but guarded by queens and jacks, the number of 4-card suits at all justifying consideration of opening bids of 2-Hearts will appreciably shrink from the above figures. Note that the 5-card and 6-card suits jointly amount to 78 per cent of all those hands given above that merit consideration of opening bids of 2-Hearts. To sum up: more than half the 4-card suits obli POWERFUL HANDS I63 gate opening bids of 2-No Trumps rather than 2 -Hearts; the suit bid on only four cards possesses no advantage over the no-trump approach for those hands lacking guards in the fourth suit; about 4 out of 5 hands allowing opening bids of 2-Hearts justify an assist by partner on 2 small trumps and a single definite trick; it would be upsetting in 4 of 5 instances to be obliged to even consider the possibility that partner does not desire you to assist his opening bid of 2-Hearts upon 3 small trumps and a sure trick. In view of the above facts giving a possible double meaning to an opening bid of 2 -Hearts is not in line with efficiency and it cannot be justified. Never make an opening bid of two on any 4.card suit. XXI THE CLUB CONVENTION THERE is a natural hiatus in ordinary contracting, due to holdings poorly shown by bids of one, either in a suit or no-trump, but failing to fully meet the more exacting requirements of opening two-bids. Various special bids have been introduced to fill this gap, such as the short suit convention, the no-trump approach, and numerous "minor suit conventions;" the best of the latter conventions is termed "the club convention" or more often, "the Vanderbilt convention." Just because followers of some other system of bidding may not need to employ this convention does not mean that they will not be asked by some partners to play it, and in any event a player should be able to understand what opposing declarations mean, even if he and his partner have no intention of using the convention. The no-trump approach possesses the advantage of utilizing only a single ambiguous declaration (The opening bid of 2-No Trumps may denote either three or all four suits guarded). The club convention necessitates several changes from normal contracting: i-No Trump must not be used if an unguarded ace is held or if any suit lies wholly unguarded (the Q X is considered sufficient, as well as i64 THE CLUB CONVENTIONS 165 any regulation stop to a suit); in place of the threesuited no-trump, I-Club is bid; unless willing to bid 2-Clubs on a hand not meeting the peculiar requirements of the conventional I-Club, you must pass; the ordinary response of I-Diamond is also barred -the hand must conform to special requirements to bid I-Diamond over partner's uncontested I-Club. As under this convention an opening bid of 2-Clubs shows only the strength required for an ordinary declaration of I-Club, you must make an opening bid of 3-Clubs in order to disclose a hand calling for an ordinary opening of 2-Club bid. At first these various departures from regulation bidding will doubtless prove confusing, and unless some great gain can be shown for the system players will not be disposed to adopt the club convention. Stated briefly, an opening bid of i-Club means as follows: I hold at least three sure tricks. I may not hold a single club in my hand. You must not leave me unrescued, if the next bidder fails to declare; if he declares you need not bid unless you choose to do so from strength. If you must rescue me, bid I-Diamond to show that you lack a minimum of two sure tricks; if you have two sure tricks bid something besides I-Diamond-bid 2-Diamonds in case you want to show strength in that suit. I may have shown my entire strength by my opening bid or I may be able to show a strong suit, or to bid for either game or slam when assured that you hold at least two sure tricks. I probably lack a twosuiter or I would have bid one of its suits. Probably I hold in reserve either a shift of suit or I can bid I66 CORRECT CONTRACT BRIDGE no-trump without injury, in case you show me the character of your hand. The various possible meanings of the opening iClub bid are clear, although nothing shows the difference between very great strength and quite moderate resources. The i-Diamond or 2-Diamond responsive bid is definite, but a take-out of i-Spade shows only that at least four spades are held and that somewhere in the hand two sure tricks may be found, without showing any stop to the run of the suit declared, which in this respect is inferior to the response to the opening bid of 2-No Trumps in the no-trump approach. The club convention does not require any specified number of tricks, it only states that at least three sure tricks must be held. As a matter of fact, a minimum of seven probable tricks at a major make or eight probable tricks at diamonds or clubs are required to make a game probable. Even four sure tricks, unless accompanied by lower honors, do not render it probable that no player will overcall an opening declaration. For hands of moderate strength I think ordinary contracting will answer about as well as the club convention; for very powerful hands, where partner is quite unlikely to hold two sure tricks, I much prefer either the short suit convention or the no-trump approach, preferably the latter. SLAM BIDDING A few geniuses may obtain rather satisfactory results without proper tools but the remainder of humanity needs things made as fool-proof as possible. The system hereafter outlined of contracting for games and slams has in its favor greater probabilities for success than any other method yet devised; it also contains fewer ambiguities and requires less individual brilliancy to operate successfully. As partnership involves intelligent co-operation, ask your partner before starting your game: "Do you understand 'slam bidding,' such as ace showing?" Unless your partner evidently thoroughly understands your proposed program, you had best limit your efforts to the less efficient but more simple tactics followed in Auction. Remembering that after a quarter of a century of Auction many players still employ Whist tactics, although calling their game Auction, you need not be surprised at the numerous Auction players who call their game Contract but who in reality are still playing the older game. Don't argue with them; they may ultimately awaken, but in the meanwhile many others are rapidly acquiring the peculiar strategy and technique best adapted to efficient contracting. I67 XXII SLAM BIDDING SIGNALS MOST Contract hands follow sound Auction bidding, except that contracting must not cease until your goal has been reached. Shun poker tactics and weak take-outs lest your partner overassist an unsound declaration; it is his duty to carry you to a probable game contract. Watch the score; keep the bidding alive; stop at game unless a slam appears almost certain; unless probably able to go game never bid for a lead against a declaration that cannot score game; unless determined to outbid opponents or unless able to penalize further contracting do not overcall a game bid if there is the least chance that you may force opponents into a successful slam declaration. Be particularly cautious of overbidding when vulnerable, with adversaries not vulnerable. Under ordinary score conditions an informatory double of one in a minor suit shows a minimum of 4 assisting tricks while a similar double of one in either major suit or i-No Trump shows not fewer than 5 assisting tricks. In responding to an informatory double in case you possess game probabilities, bid one trick higher than needed, to indicate that fact. i68 SLAM BIDDING SIGNALS I69 Expert slam bidding employs declarations unknown in Auction. Of course the joint twenty-six cards of a side must count enough tricks to justify slam hopes or attempts at slams are sheer folly. Just because your side can count 12 or 13 tricks is not enough, the hands must "fit," so that some weak point in your holdings cannot defeat your contract. The signals peculiar to Contract definitely disclose your safe limits of endeavor, disclosing the tricks that cannot be lost or the tricks that must be lost. Proper slam bidding tactics are both more efficient than trick counting alone and also more enjoyable. "Ace showing" and similar tactics are never decried by any player thoroughly understanding slam bidding, unless for reasons of his own he adheres to some system, more typical of Auction than of Contract, that fails to provide a place for slam bidding tactics. Slams are rarely possible at no-trump, or against a player who has made the opening bid, or at any secondary declaration of your partner. SLAM SIGNALS A trump declaration of two when made by the opening bidder announces "game expectations and slam hopes." Partner is expected to assist upon two little trumps in case he holds even a single definite trick (An ace, or K Q, or the kings of two suits). Sometimes greater side strength may condone an assist upon a singleton trump but added length of trumps never excuses an assist, or 170 CORRECT CONTRACT BRIDGE "courtesy raise," without at least a single definite trick. The slam signal also may be given as follows: by a forced bid one trick higher than required; by jumping partner's opening bid of one to three; by bidding a suit already named by an opponent, provided your partner has already made a suit declaration. In general a slam signal by the original declarer of a suit indicates the ace and a trump suit sufficiently solid to avoid the loss of more than a single trump trick (Five trumps including four honors or six trumps headed by A K Q or A Q J). Opening bids of two require in major suits probable ability to win a minimum of seven tricks; similar bids in minor suits indicate probable ability to win at least eight tricks. Greater total strength than stated above, or a hand containing at least five sure tricks divided among not less than three suits and better adapted to a trump than a no-trump make, may justify an opening bid of a 5-card suit that is less solid than required above. A slam signal by the assisting hand requires a minimum of six assisting tricks and better than average trump support. An opening bid of 2-No Trumps is merely a game signal; it rarely anticipates a slam. The great majority of slam signals result in contracting running no higher than game, but many hands without slam hopes (Due to lack of aces or to the openness of the trump suit) urge employment of slam signals, followed by the "reverse signal." SLAM BIDDING SIGNALS I71 THE STOP SIGNAL Bidding the game contract, instead of showing side strength, announces bidder's opinion that a slam appears too dangerous to attempt. Unless his partner can see a certain little slam and is merely hoping for a grand slam, he should cease bidding. The following hand that I recently encountered well illustrates the danger of not heeding the stop signal. A Q J I V 642 987643 0 5 653 Y [ K9 72 v KQJ85 3 A B v AI7 * KQJ *A A 0 8 Z 0 AKQJ xo A84 9 * 10 5 2 0 976432 Contracting of the above hand went as follows: Z, Pass; A, i-Heart; Y, Pass; B, 3-Hearts, an absolute demand for me to show any side ace held; Z, Pass; A, 4-Hearts, thus denying holding the missing A A. Fortunately my partner had the sense to pass, as the opening lead caused us to lose three spade tricks; after which we fulfilled our contract of 4-Hearts. Occurrences like this long ago de 172 CORRECT CONTRACT BRIDGE stroyed my faith in trick counting for slams and caused me to adopt "ace showing." THE REVERSE SIGNAL A pilot must have a reverse signal. Having given a slam signal, to insure an assist by a partner holding a minimum of two small trumps and one sure trick, the original bidder often wishes to stop contracting at game, usually because his trumps contain more than the one loser that his opening twobid signifies. The reverse signal is merely a stop signal when employed by the original bidder, given by naming just game instead of showing his lowest side ace. The following hand illustrates a case of this sort, * 52 v Io 8 42 4 64 0 A J Io 8 3 6 9 6 Y 4 A J IO843 v KJ76 A B vAQ * K9832 * AQJ 0 72 Z 0 KQ KQ7 9 953 * 107 5 9654 Contracting of the above hand went: B, made an opening bid of 2-Spades, lacking the following important cards, A K Q, K, 4 K and OA; unless A has at least one sure trick, either the missing SLAM BIDDING SIGNALS 173 ace, the two missing trump honors, or two of the three kings missing, B does not want to try for game. If A has one sure trick game probably can be made, so B opens with a bid of two. His partner having the one required trick bids 3-Spades. Instead of bidding 4-Clubs and having A respond with 5-Clubs, B ends the contracting with 4-Spades. SHOWING ACES "Showing an ace" means making a bid of a side suit containing an ace. You cannot show an ace unless you and your partner have previously agreed upon a trump make and unless one of you has also given the slam signal. There must, of course, be a way left open for a denial of aid for partner's make and for a proposal to substitute another declaration: if you open the bidding with 2-Hearts (Announcing game expectations and slam hopes), if your partner shifts either to 2-Spades or 3-Clubs he is not showing the ace of the suit that he bidsyour partner is offering a suggestion that his declaration be substituted for your make. But if your partner answers your opening bid of 2-Hearts, by bidding 3-Hearts, you have both agreed upon hearts as trumps, hence a later bid of any other suit by either of you shows the ace of the side suit subsequently bid. Partner's raise of your original bid, to one trick short of game, or, if necessary, to one trick more than game, so as to avoid the stop signal indicated by bidding just a game contract, asks: "Partner, what is your lowest side ace?" As your only possi I74 CORRECT CONTRACT BRIDGE ble answer to that question, you bid the suit containing that ace, knowing that your partner will not leave you in that make (Bidding 3-Spades, for example, instead of either 4-Clubs or 4-Diamonds, over your partner's jump to 3-Hearts of your opening bid of i-Heart, denies that you hold either of those minor aces). SHOWING KINGS AND QUEENS While it may seldom be required, hands do appear where showing kings and queens affords the only hope of definitely determining whether or not a slam is safe to bid. The next hand illustrates this feature. Bidding a suit of which your side has already shown the ace, shows possession of the king; another bid of that suit shows possesion of the queen. 863 v' KQJ65 * KQJ OAK 4 9 7 Y J 5 4 84 A B 9 4 A983 4 1 o642 0 O 8753 Z 0 Q942 4 AKQ2 V A I07 3 2 4 75 0 J6 Z opened the bidding on the above hand with IHeart, intending to show his shorter spade suit SLAM BIDDING SIGNALS I75 later on, if needed, but Y's jump to 3-Hearts demanded ace showing, so that Z's response of 3 -Spades showed only possession of the ace of the suit named, also denying thereby having the missing 4* A. There still remaining a chance that a slam might be made, Y bid 4-Diamonds. To this Z replied with 4-Spades. Y was then perfectly safe in retorting with 5-Diamonds as the contracting to date had shown that only a single club and perhaps one spade trick could be lost. In reply to Y's 5 -Diamonds, that bidder knew that Z might respond with 5-Hearts, to show that he had exhausted features to disclose, or Z could bid 6-Diamonds to show the queen of that suit, which would allow a discard of Y's losing spade. Instead of bidding 5 -Hearts, Z showed his queen by bidding 5-Spades. Now certain of a little slam, Y ended the contracting with 6-Hearts. BIDDING OPPONENT' S SUIT Having previously announced the make at which your side is to play, a subsequent bid of opponent's suit states that no tricks of that suit can be lost, provided your side obtains the contract at its own suit. If, for example, you open the bidding with I-Heart and are overcalled by I-Spade, your partner's bid of 2-Spades is a slam signal, announcing no losers in spades (Provided you play the hand at hearts) and also stating that your partner is strong in hearts. Frequently the most welcome information that could be given you is that your partner holds no loser of an opposing suit. You do not care if he is 176 CORRECT CONTRACT BRIDGE void of that suit or holds its top cards. In some special case he may even risk considering possession of the adverse A-Q, back of the bidder of a suit, as showing no loser. Regardless of the fact that some writer may condone bidding an A-X of an opposing suit, to show what he calls "a first trick winner," such misleading contracting is neither sound nor sensible. If your partner thinks that his possession of the A-X or K-X of an opposing suit insures the loss of only a single trick of that suit, provided the balance of the contracting justifies the belief that no other trick can be lost, let him venture a contract of a little slam, but he must never bid opponent's suit when his holding includes even a single loser of that suit. 4 A V K8 32 * 93 0 K Q J iog 9 ^ KQJIo74 y * 963 V7 A B V 9 6 4 io 8 2 A 4 * J 7 6 54 0 A75 z 0863 4 852 IV A Q J IO 4 * AKQ 0 42 Contracting of the above hand went: Z, 2-Hearts; A, 2-Spades; Y, 3-Spades (To show strong heart aid, absence of spade losers, and a belief in the probability of a slam); B, pass; Z, with SLAM BIDDING SIGNALS 177 his mind relieved of the possible loss of spade tricks, 4-Clubs; A, pass; Y, having no side ace to show, 4 -Spades, to discover whether his partner held the missing ace or would show the king of clubs; B, pass; Z, 5-Clubs; A, pass; Y, now certain of a little slam but no more, 6-Hearts. SHOWING A TWO-SUITER If partner fails to aid your first make, or in case he raises your first bid of one only a single trick, your second suit may be shown, to afford partner a choice of declarations. Neither of you having given the slam signal plainly indicates that your second bid is not intended to show an ace, you evidently are showing a two-suiter. As the hand below illustrates, sometimes such strategy results in a notable gain. 952; K763 4 K3 0 KJ52 a KJ87 Y a 4 v IO 4 A B J 2 J 7 6 4 F* Io 982 0 A Io7 0 Q98643 4 A Q o 6 3 v A Q 9 8 5 * AQ5 0 -Z's opening bid was I-Spade, which Y raised only to 2-Spades, justifying Z in showing his second suit by a bid of 3-Hearts; preferring the second suit, Y bid 4-Hearts (The stop signal). As Z's hand 178 CORRECT CONTRACT BRIDGE counts 8Y4 tricks at hearts and as his partner has shown at least 4 tricks by his assist of both suits, Z's final declaration of 6-Hearts could not be criticized. By discarding one of dummy's spades on a good club, and ruffing two spades, Z just fulfilled his contract. SHOWING A SUIT Provided one partner or the other has first given the slam signal, so that the meaning of a subsequent declaration cannot be mistaken as offering a shift of declaration, an unnecessarily high bid of a side suit shows absence of losing cards in that suit. If you first assist your partner's opening bid of two, he cannot mistake a later unnecessarily high bid of your side suit for anything besides showing no losers of that suit. If your partner at once aids your opening bid of two, or in case your partner jumps your opening bid of one, to three, your subsequent needlessly high bid of another suit must be read as showing that you have no losers of that suit. 9763 V Q J Io 6 3 5 0 io 8 6 4 542 Y AQJ io v[ A A B v52 4 A Io7643 KQ J 2 o QJ2 Z OAK K8 K9 K9874 8 0 97543 SLAM BIDDING SIGNALS I79 The above hand affords an example that I recently noted of the occasional utility of showing no losers in a side suit. Contracting went: Z, pass; A, i-Club; neither Y nor Z figured thereafter; B, 3-Clubs, knowing that game must be certain and hoping for a grand slam; A, 4-Hearts (To show no heart losers). Here is a point worthy of note: while it is considered obligatory for the partner who responds to the slam signal to show his aces in order, sometimes strategy condones the player giving the slam signal when he shows a higher ace, without mentioning a lower one first; all that B wanted was to discover whether his partner held the missing A K, so B bid 4-Spades, instead of making a futile bid of 5-Diamonds, to inquire whether A could bid 5-Spades. A was obliged to respond with 5-Clubs, which B carried to 6-Clubsall that the hand could win. XXIII THE FIT OF HANDS A VERAGE values frequently are either too great or too small to yield satisfactory results on particular hands that are bid solely upon the number of probable tricks that each partner can count. While the method herein given for valuing hands is superior to any other, no possible system of hand valuation is wholly dependable beyond about ten tricks. More than two-thirds of the big hands held -the critical hands that offer the lure of probable slams-are either overbid or else underbid by the ablest of trick-counters. More important than hand valuation is the question of "the fit" of partners' holdings. Just the extent to which the cards of one partner complement the deficiencies of the holdings of the other partner determines the proper contract. Only slam bidding tactics are sufficiently definite to employ with critical hands. Usually the special declarations already described are sufficient to determine the profitable bidding limit, but sometimes less well known tactics must be utilized to make clear the last feature desired by an intelligent partner. The following hand recently appeared. It is interesting from the acumen displayed by my partner (B), who showed himself to be too hard-boiled to i80 THE FIT OF HANDS i8I risk a guess at anything-he had to be shown. Although my hand counted 7Y2 probable tricks, I considered that the spades scarcely justified more than my opening bid of I-Spade. My partner's hand counted 82 probable tricks yet he knew that a grand slam might be impossible in case I lacked both the O A and the Q2 K; it must be absolutely impossible if I did not hold the a A. Even a little slam might be missed in case I was short two of those three important factors. As may readily be seen, an exchange of my 0 A for the 4 A would spoil a grand slam, although the probable tricks would remain unchanged. A little thought will show other changes in the honors of suits that might spoil chances for a slam although the trick count would not be altered. The fit had to be demonstrated, to eliminate the guessing employed by most bidders. J8 v J963 4 K972 0 643 4 AKQ64 Y Io 9752 V K8 A AQ Q4 J643 B - O A8 O KQJ Io9 3 V Io 7 5 2 A Q io 8 5 0 752 182 CORRECT CONTRACT BRIDGE Contracting went as follows: A, i-Spade; B, 3 -Spades, which demanded a bid of the lowest suit of which I held the ace; A, 4-Diamonds; B, although I had denied holding the e4 A, evidently was satisfied that slam chances were not impaired thereby, because he bid 4-Hearts; A, 5-Hearts; B showed that the contracting thus far proved to him that a little slam could be made, as he bid 6-Clubs. Note the two rules given below: i. After the slam signal has been given, either an unnecessarily high bid of a side suit, or bidding that suit out of its regular order, states that no losing cards of that suit are held; 2. Unless a bidder knows from the previous contracting that a little slam can be made, he must never bid six in a side suit; the bid of a little slam in a side suit asks partner to bid a grand slam in trumps, provided he can see one vital undisclosed feature justifying such a declaration. This was the situation: I had opened the contract with only i-Spade; my partner had announced game expectations and slam hopes, by jumping the bid to 3-Spades; I had then denied having the 4 A, but I had stated that I held the 0 A and the V K; my partner had stated only that he held the V A and no losers in the club suit. His last bid of a little slam in clubs stated that he could find no losing cards in either hearts, clubs, or diamonds. Evi. dently he wanted me to decide whether or not my spades were good enough to justify a bid of 7 -Spades (For all my partner knew I might be bid THE FIT OF HANDS I83 ding on a suit headed by A-Q or K-Q. The situation being perfectly clear, I terminated the contracting with 7-Spades. The hand below also illustrates the proper employment of a 6-bid in a side suit, to oblige partner to decide whether a little slam or a grand slam should be the contract. AK2 2 AK9863 * 43 0 A4 * 97643 Y [ Q J io8 5 4 A 2 4 J 6 B 9852 > J o963 Z O KQ8 4 -Q Q J Io 7 5 4 A K Q Io 7 0 752 Contracting went: Z, I-Club; Y, 2-Hearts; Z, 3-Hearts; Y, 4-Diamonds; Z, 5-Clubs; Y, 5-Spades. Z can now see a certain little slam; in case Y holds either the 0 K or the A K, a grand slam appears assured, so Z, by bidding 6-Clubs, "asks the question," whether Y holds an added important feature not yet disclosed. Y has not yet shown his A K, so he confidently bids 7-Hearts. No possible system of contracting is anything like infallible. At times hands fit better than the bidding discloses; such a hand is given below. Counting within two tricks of game in his own 184 CORRECT CONTRACT BRIDGE hand, and lacking the ace of trumps, Z opened the contracting with 5-Clubs. Of course Y raised this to 6-Clubs. 4 QJ9862 vc AK4 * A4 063 A A K IO 5 Y * 7 4 3 v Q Io 8653 A J 7 48 3 0o05 Z O KQ98742 4 - 92 4 K Q J IO 97652 0 AJ The opening lead of A's 4 K gave the declarer a grand slam, but no player could have anticipated such an event. As eleven trumps between two hands usually gives each opponent one trump, Z calculated that by reserving his deuce and trumping the first trick with a higher club, he might find that dummy could be put in the lead twice with clubs and twice with hearts, affording Z an opportunity for a grand slam through the final establishment of Y's spades. As this worked out in play, Z made a grand slam. The next hand shows a novel declaration with a partner whom I considered sharp enough to grasp the meaning of my continual reversion to bids of my opponent's suit, of which my partner had already stated that he held no losers. I was obliged to THE FIT OF HANDS make my partner bid until he told me that he held both the major suit aces. A86 V AQ64 A Q J o 8 5 0 — 4 9542 Y o 7 v 9853 A B v K Io 7 2 4 - 4 O JIO762 Z O AKQ843 * KQJ3 l J 4 K97632 0 95 I dealt the above hand and passed. A also passed, but my partner opened the bidding with 2-Clubs, which B overcalled with 2-Diamonds, after which neither opponent bid. I bid 3-Clubs; Y went 3-Diamonds, to show no losing cards of that suitthe thing I most needed to know. I feared that if I kept bidding clubs I might discourage my partner from showing me enough to justify a slam bid of some sort, so I urged Y to show aces, by my bid of 4-Diamonds. Y caught the idea that I had something good to show in due season, so he bid 4-Hearts; lacking the king of this last suit I bid 5 -Diamonds. Y next bid s-Spades, knowing that I must see a little slam or I never would force himo to bid another side suit. Now certain of a grand slam, I bid 7-Clubs. 186 CORRECT CONTRACT BRIDGE SAFETY FIRST Ordinarily you must bid a game that you can count in your own hand. Reserve slam attempts for occasions that cannot jeopardize the scoring of game. When Z opened the bidding with I-Heart, of course A knew without being told that Z must hold the K-Q of both hearts and spades; with ten tricks in his own hand he was obliged to bid 3-No Trumps. The way that he made a little slam was the only thing noteworthy about the hand. 9742 IO 82 4 J97 0 654 A A 5 Y 4I 8 6 3 A A93 J 5 ^ AKQ A B 4 6542 0 AKQJ7 Z 0832 K QJ K Q 764 Io8 3 O Io 9 Y's opening lead was the C Io, on which went B's J, Z's Q and A's ace. Starting to run out diamonds, the declarer noted that the fall of Z's 10-9 made an entry to dummy of B's 0 8; if each opponent held just three clubs it would be possible to make a small slam, so A led three rounds of clubs and found that he had established a long club in dummy. Entering dummy by leading his 0 7, the THE FIT OF HANDS 187 declarer secured a discard of his only losing spade, by leading dummy's good club. Then he led dummy's last heart through Z, giving opponents only one trick. SHOWING ALL SIDE ACES Under certain prescribed conditions, all side aces that are missing from partner's hand may be shown by a no-trump bid. This economy of bids frequently results in ability to show slam certainties not otherwise possible to disclose. Having first assisted partner's suit bid in response to his slam signal, your subsequent shift to no-trump announces possession of all side aces, allowing partner to show kings. The following hand illustrates a case where a little slam contract is made safe by above procedure, whereas any other style of contracting involves guessing. 4 A72 v 7632 * A8 0 AK64 4 109654 Y 4 KQJ83 V K5 A B V 4 J 7 A * 109642 O J IO 93 0 72 4 - %v A Q J io 9 8 * KQ53 0 Q85 188 CORRECT CONTRACT BRIDGE Contracting of the above hand went: Z, 2-Hearts; Y, 3-Hearts; Z, 4-Hearts; Y, disregarding the stop signal, showed his three side aces by bidding 4-No Trumps; Z, 5-Clubs; Y, 5-Diamonds. As Y had shown the A A, the 4 A and the 0 A-K, Z knew that the only possible losing trick must be in case A held the missing king of trumps, so Z bid and made a little slam at hearts. BIDDING NO-TRUMP SLAMS The two most prolific sources of loss to those who understand hand valuation and sound play are failure to employ slam bidding at trump makes and attempts to bid no-trump slams without a thoroughly established long suit in one hand. The next hand shows holdings justifying a grand slam being bid by the assisting hand, without attempting to show just what is held by each partner. * 9854 v J9872 45 0 K Q4 4 QJ2 Y AAK3 v K Q o A B A3 4 Io 98 2 A K Q J 7 4 OAJ8 Z 053 * Io076 0 Io 9 7 6 2 THE FIT OF HANDS I89 A was a reliable bidder. He opened the contracting with I-No Trump. I held B's cards. I could not imagine my partner having less than the A Q, (2 K-Q and O A. As such holding would allow me to discard my losing diamond, and as my clubs were almost certainly thoroughly established, I could see no losers, and I jumped the contract to 7-No Trumps, which of course was made. PUZZLING HANDS Close questions at Contract ordinarily prove more troublesome than similar situations did at Auction -due to the greater rewards and penalties of the newer game, also to the inability to profit by games and slams unless contracted. Contract is still largely an undeveloped science, with many of the best Auction players working overtime guessing at what constitutes proper procedure. Superficial players may not care to read the chapters that follow, which are intended to aid the more serious players to think logically on new and important topics. 190 XXIV DETERMINING PROBABLE RESULTS M ANY shrewd players sense whether the majority of hands possess game prospects. I have yet to meet one able to distinguish between the hands that barely exceed game probabilities and those that fall just short of such prospects. The determination of game probabilities is really absurdly simple, provided you employ only the method of ob. taining the true values of hands given in Chapter IV. Outside of Bridge, naivete often charms, but the artless partner who expects to obtain correct results, without employing fractions of tricks, belongs in Arcadia. During the Victorian period, Bridge Whist commenced to supersede Whist. The newer game required either the dealer or his partner to name the declaration; there was no competitive bidding. Knowing nothing of card values, players of Bridge Whist resorted to rules framed by mathematicians, guiding the namer of the make to choose between no-trump, a suit call, or naming spades on an impotent hand. The rules followed were not intended to show the number of tricks that could be won; they were designed only as props for players hopeI9I 192 CORRECT CONTRACT BRIDGE lessly ignorant of hand valuation. Like children, the majority of players followed whatever was most simple, regardless of its efficiency. Shunning the more accurate methods for those requiring less mental effort to apply, the rules in common use often were shockingly crude. THE POINT SYSTEM The most generally accepted method of determining no-trump makes was the "point system." Apparently none of the calculators of the different systems bothered to tell what his points represented and no player thought of inquiring. The late W. H. Whitfeld called an ace o points, king 7 points, etc. Edmund Robertson assigned 7 points to the ace and 5 points to a king, et cetera. Captain H. M. Beasley gave the correct relative values employed in this work: A, 6 points; K, 4 points; Q, 3 points; J, 2 points; Io, I point. If players like, they may count their points as Captain Beasley did, then dividing the total result by 4 will give the probable trick value of the hand. But each point is just onefourth trick; it is impossible to avoid the use of fractional values, call them what you choose. Because it was born in a bird-cage a mouse cannot be termed a canary. In any sound system the king has the value of a full probable trick; other honors possess fractional values. For example, the long abandoned system in which A-4, K-=3, Q —2, and J=i, has been rescued from a worthy oblivion and attempts are being made to adapt these incorrect proportions of PROBABLE RESULTS I93 tricks to the use of Contract bidders. In this systern each point is really one-third of a trick; although you may choose to call them certain numbers of points the A=i 1/3, the K =i, the Q=2/3, and the J =1/3 trick. Many players have a mistaken notion that the ace is the honor worth the probable trick. Of course such an error causes 4 points to be the full trick value; this makes a big difference when counting the probable trick value of a hand, as the two hands below will illustrate. A K J IO 5 v AQ9 * QJ8 0 A J 7 AQio3 v A Q IO 9 * A6 0 A Q 5 The real value of the first hand is 7 4 probable tricks: the point system accords that hand i8 points; using the king as the full trick the hand is reckoned as worth 6 tricks, which is a trifle more than a trick short of actual strength; calling the ace a full trick causes the hand to blie counted for only 4X2 tricks, which is wholly unreasonable. The real value of the second hand is 8 3/4 probable tricks: calling the king the full trick, the 22 point count of the hand is equivalent to 7 1/3 tricks; if the ace is called the trick, the second hand must be valued at only 5>2 tricks-more than 3 full tricks short of its actual value. Finding that the "4-3-2-I" count is too far off to yield satisfactory results, instead of accepting the actual values of 6-4-3-2-I for the honors, some writers are now employing the 5-4-3-2-I point counts for the five honors. Of course this is an improvement over the 4-3-2-1 point system, but for accurate work I94 CORRECT CONTRACT BRIDGE the ace should be given the true value of 6 points or i Y2 probable tricks. Give yourself a chance to bid what your cards are worth, by employing real values. If an educator deems it best for awhile to employ something that he considers most simple, although faulty, to bring his subject well within the comprehension of his audience, that is solely the business of himself and his hearers. Many parents prefer delicate fictions for their children, instead of the plain truths that many others tell their offspring from the start. But at some period youth has to abandon tales of Santa Claus, cabbages, and storks, for realities. The sole question with both children and Bridge players may be when shall the real facts be told. In Contract, at least, I prefer the truth from the first; half truths never make real players of students. PARTNER S PROBABLE STRENGTH To bid to the best possible advantage you must first learn to value correctly any hand that you may hold; next you must be able to properly ascertain the probable strength held by your partner; the total strength held by your side fixes your chances for game or slam. On an average, the four players unitedly hold cards worth I5 honor tricks, as either declarer or dummy, the values held by the defenders reducing to only sure tricks. To determine the values held by your partner you deduct from 5 the honor tricks PROBABLE RESULTS I95 that you have. The remainder at once gives you the probable tricks (As viewed by declarer or dummy held by the three other players). One-third of the tricks held by the other three players gives the average number of honor tricks held by any single player (As your partner), but you must not trust this shifting average; you must consider only what your partner probably holds. There is a distinct difference between an average holding and a probable holding, as the following results of calculations show. As 20 honors average to yield only 15 trizks, sometimes several honors are required to yield one trick. Without appreciably affecting the relative chances to be calculated, it will save an enormous amount of labor to consider each trick as if it were a single card, instead of consisting in some cases of two or even three honors. Considering each trick as a single unit, in case you hold just 5 honor tricks, your partner's average holdings will be I/3 x 10 = 3 I/3 tricks in honors. But your partner has 264 chances in Iooo to hold fewer than 3 tricks and 736 chances to give you 3 or more tricks. In case your low trumps are worth 2 added tricks at major makes or 3 more tricks at minor makes, the chances are that your joint holdings will result in game for your side. If you hold just 6 honor tricks, leaving 9 probable tricks to be divided among the three other players, the average holding expected of your partner is just 3 tricks. But you must not assume that your side 196 CORRECT CONTRACT BRIDGE probably can go game at no-trump or, if your trumps bring the total value of your hand up to 7 tricks, that game is probable at spades. You must consider the probabilities. Out of iooo1000 such instances your partner will hold; Fewer than 3 tricks 352 times Just 3 tricks 310 " More than 3 tricks 338 " 1000 If you open the bidding with one, there are 352 chances that you will be better off than had you bid more. There are 310 cases when your one bid may cost you game, because your partner will not assist; there are 338 chances that he will assist your one bid, so that you will bid game. With chances of 690 that an opening bid of one will be the best for you to make, why bid more when you prefer a small score to being penalized? If you hold just 7 honor tricks, the chances for your partner to hold various numbers of tricks are as follows: Under 2 tricks, i 64 in 1000; 2 or more tricks, 836 in iooo1000. As the average expected of partner is only 2 2/3 tricks, the probabilities that he will hold 3 honor tricks need not even be considsidered. If you need only 2 tricks from partner to go game, at any make, consider that he will probably have them and open the bidding with two, on slam prospects, or else bid game at once. PROBABLE RESULTS I97 THE RULE OF THREE Divide by 3 the total honor tricks missing jrom your hand. Unless the one-third average obtained slightly exceeds the amount you require for game, you lack game probabilities. Experienced players often know without rules whether the best opening bid is one, two, or more. Less well trained bidders require more definite information to steady their contracting. The following hands illustrate proper opening bids on hands of differing types. AKIo8654 - 4 2 0KQJ o5 The above hand contains 5Y4 honor tricks and has a total strength of io probable tricks. There are just three vital cards missing that are needed for a grand slam (4 Q, 4 A, and 0 A). Partner's chances in 703 to hold these essential honors are: to hold none, 200; just one, 325; just two, I56; to have all three, 22. To jeopardize an almost certain game for such meager chances of making a slam would be poor strategy. The proper opening bid is 4-Spades. The right opening bid on the next hand shown is 3-Hearts: 4 6 V AQJ8653 * K72 0 96 The hand has a probable value of just seven tricks, asking partner to win two tricks for fulfillment of contract and to assist, regardless of trump strength, upon three probable tricks. Applying your rule of three, you note that partner should have I98 CORRECT CONTRACT BRIDGE the needed help to assist. Under such circumstances an opening bid of 4-Hearts would not be severely criticized; the chief objection to the game bid is that an active partner with more than three assisting tricks might jump the bid to 6-Hearts, which probably cannot be made. What should be bid on the next hand? AKQJIo5 V AJ84 4 - 0 852 The value of the hand is 8 probable tricks, which is not enough for game without assistance. The honor values total 6 tricks, leaving 9 tricks to be divided among the remaining three players. The rule of three assures you that partner should hold at least the 2 tricks needed for game. With game probabilities and slam hopes, the opening bid should be held down to 2-Spades. There seems no justification for the often heard remark: "An opening bid of two shows honors in at least three suits." Observation shows that notion to be held chiefly by players who are unfamiliar with slam bidding tactics, especially those who have adopted the short suit system, perhaps without much thought. Certainly the next hand distinctly calls for an opening bid of 2-Hearts, instead of either one or three. A Q J I 5 A Q J Io 5 2 4 0 7 With only 6 honor tricks, partner should hold at least 2 tricks. The whole hand is worth 8% probable tricks, making game reasonably certain if partner can assist on two small trumps and a single definite trick. PROBABLE RESULTS I99 PROBABLE GAME CHANCES WHEN AN OPPONENT HAS BID If an opponent has opened the contracting you had best credit him with 5 honor tricks. The total honor tricks held by you, plus 5, when deducted from IS, give the honor tricks probably divided between the two remaining players. Suppose that this difference amounts to 4 tricks. Chances in IOOO for your partner to hold various numbers of these missing tricks are as follows: none, 49; I, 248; 2, 406; 3, 248; all 4, 49. As there are precisely even chances whether your partner or your opponent holds more than two honor tricks, your only plan is to note whether your partner's chances for game appear reasonable in case he has only one or two honor tricks. Suppose we take the hand shown next, when Z has opened with a bid of i-Club, and A considers the chances for game on a response to his informatory double. K K8654 C 97 4 72 0 IO 9 7 5 & AJ92 Q io v K Q Io 4 A B J862 4 6 4 Q J Io5 3 0AQ63 Z J4 73 v A53 4 AK984 0 K82 200 CORRECT CONTRACT BRIDGE A has 6~4 honor tricks, with an ideal distribution for a double. Also A can add at least i Y2 trump tricks to his values (>2 trick for 4 trumps and one trick for ability to ruff clubs once), a total probable assistance for any response of 7 Y4 tricks. Aside from honor tricks, ordinarily A may reasonably expect to find his partner with a i-card suit, which in itself counts i 2 probable tricks, as more often than not the opposing 4 trumps will fall in two rounds. With this in mind A may reasonably expect his partner to go game at either major suit, even if his partner holds no more than a single honor trick. As the cards lie, whether B or Y happened to be A's partner, game should result as a response to A's informatory double. xxv THE TWO-NO TRUMP APPROACH IN the long run, the player who wins most is he who habitually bids what the situation and his values direct. He will encounter more croppers than the timorous player, but he will not miss the games and rubbers that timidity loses. Great strength about evenly distributed among three or four short suits requires a strong forcing bid, rather than a weak suit approach. Think of the joint 26 cards of your side, rather than view your prospects from the narrow outlook of your own 13 cards. When you make an informatory double of an opening bid of i-Diamond, instead of at once bidding the following hand, you ask your partner's opinion concerning the best declaration of your side: 4 AQJ6 v AK94 4 KQJ8 0 5 In case you hold the above hand when no adverse declaration has been made, real team work is for you to ask your partner to name his choice of declaration. If you open the contracting with either 2-Spades or 2-Hearts, because you deem your hand too strong for an opening bid of one, there are 7 in io chances that your partner will hold fewer than four cards of your suit, which under the short suit 20I 202 CORRECT CONTRACT BRIDGE convention does not justify an assist, even though your partner holds the one definite trick needed to raise. But in case you allow your partner to name the suit make you nearly treble his chances of holding four or more cards of one of your three good suits, and he has even chances of having five or more cards. As aid to your partner's best make your hand averages to be worth iy2 tricks stronger than it will be in case you become the declarer; the strength of your joint cards averages to be three tricks greater on your partner's make than on your own choice. Contrary to popular belief, holdings having the best game chances and the greatest slam hopes are not those with numerous high cards held in short suits; game expectations and slam hopes are strongest with powerful trump suits and modest side strength, because they ask no trump support from partner and because they afford him probable chances to hold enough side tricks to yield gamepossibly even a slam. Be not deceived by the number of sure tricks that you hold or by your numerous honor tricks-you must consider the probable strength of the entire 26 cards of your side. By using the opening approach bid of 2-No Trumps, as you would employ an informatory double against an adverse opening make, as an imperative demand on your partner to make his best declaration, you will most often arrive at the best call for your side. About 3 in 4 declarations can better be played at some suit than at no-trump. As about 4 of 5 TWO-NO TRUMP APPROACH 203 hands justifying opening bids of two of a suit are made on holdings asking only side strength of partner, an opening bid of 2-No Trumps cannot be mistaken for anything except a demand for partner to bid-this latest and most efficient forcing bid is also the strongest one that can be offered. Of course an opening bid of i-No Trump neither seeks nor condones a weak take-out, but when you are sufficiently strong to justify an opening bid of 2-No Trumps, either you must be able to continue your contracting of no-trump, in case your partner bids your weakest suit, or else you are able to support your partner's suit make, so that game will probably result. Again remember that Contract procedure must often radically differ from what was considered ideal at the old game of Auction Bridge. Once accustom yourself to the Contract idea of the 2-No Trump approach on very powerful hands, with ideal distribution among the suits, and never again will you want to play the short suit system. This convention of employing an opening 2-No Trump as a forcing bid, does not in the least conflict with the more ordinary use of the 2-No Trumps (See Chapter VII), so long as your partner knows that you desire him to take-out or to assist in accordance with the rules given in this chapter. If your hand fails to meet the rigid requirements of an opening bid of 2-No Trumps, either content yourself with bidding i-No Trump or else bid one in your best suit. In case you require less than an ace or its equivalent for game, you may bid 3-No Trumps on four guarded suits, trusting your partner 204 CORRECT CONTRACT BRIDGE for a single trick of some sort, to give you game, just as you have to trust him all through the game. When you have one worthless suit, an ideal card distribution is 4-4-4-I; if you must play the hand at no-trump, you want a minimum of one small card of partner's best suit; in case you are to play the hand at your partner's best suit the more cards you have of that suit and the shorter you are in your worthless suit, the better your hand will fit with his: as your partner is equally likely to select as trumps anyone of your three good suits, in the long run having four cards of each good suit more often works out to your advantage than any other distribution on which you do not wish to declare a suit. For satisfactory results you should hold a minimum of 5 sure tricks or 7 honor tricks, with strength well divided among at least three suits. The further you wander from those standards, the less dependable your results will be. In case your opening bid of 2-No Trumps is of proper strength, your chances for partner to go game are excellent, provided his cards are worth a minimum of two probable tricks at a major suit or three tricks in case he must bid one of the minor suits. TAKING OUT 2-NO TRUMPS Employment of the 2-No Trump approach eliminates all ambiguity when you make an opening suit bid of two; your partner knows that you will never bid two on any short suit and consequently that he TWO-NO TRUMP APPROACH 205 may assist your opening suit bid of two on a single definite trick and two small trumps. As the opening two bid states that probably the declarer cans lose only a single trump trick, his partner may take a chance and assist with a lone trump, provided he holds more than the one sure trick needed to assist and at the same time can neither bid his best suit nor shift to 2-No Trumps. The opening bid of 2-No Trumps must always be taken as a signal for definite action, unless your partner has a wholly worthless hand; then he leaves you in your 2-No Trumps. Had you bid two of a suit, your partner under the short suit convention, would be obliged to shift you to 2-No Trumps on a worthless hand. But if your partner is trickless, you are better off at the 2-No Trumps bid by you than you are in case he bids the 2-No Trumps, because in the former case the strong hand remains closed and the opening lead comes up to your strength, instead of going through it. When your partner opens with a bid of 2-No Trumps, proceed as follows: i. Bid three of any 5-card suit stopped at least once or any 4-card suit stopped twice; 2. Honors in all four suits make 3-No Trumps preferable to a minor suit make at a love score; 3. Lacking a biddable suit, one sure trick or three probable tricks justifies a raise to 3-No Trumps; 4. Two trickless 5-card suits or a trickless suit of at least 6 cards obligate a take-out; 5. Otherwise than specified above, a trickless hand necessitates a pass. 206 CORRECT CONTRACT BRIDGE Players should accept illustrative hands as examples for procedure, rather than as proofs of the correctness of any hypothesis set forth. After the 13 cards of a single hand have been determined, the remaining 39 cards may be dealt into 8,122,425,444 different hands, so that almost any diligent advocate of a theory, whether right or wrong, should have little trouble in offering many hands appearing to support his views. Probabilities-not special examples-determine correct procedure. The following deal that I just saw made proves nothing; it is offered merely as an illustration of proper handling of opening bids of 2-No Trumps and proper action by the opening bidder's partner. 6 v 852 * QJ732 0 J 10 4 2 I Jio872 Y KQ9 J 9 A B Q Q 074 L I 4 * 9 5 0 AK97 Z 0 Q653 4 A543 vQ AK63 4 AK86 0 8 Although Z holds only 6Y2 honor tricks, the ideal pattern of his hand obligated his opening bid of 2 -No Trumps. Y's hand counts 3 4 probable tricks with clubs as trumps, and he bid 3-Clubs. As aid for a club make, Z's cards are worth 8 probable TWO-NO TRUMP APPROACH 207 tricks, so he ended the contracting with 5-Clubs, which Y just made. We will assume that A and Y had their cards exchanged. The proper responsive declaration would be 3-Spades, which Z would carry to 4-Spades, resulting in game. Had the hands of Y and B been exchanged, the hand would be played at 3-No Trumps, and game must result. As the cards were dealt in the hand shown below Y bid 3-Diamonds over Z's opening bid of 2-No Trumps. Z raised to 4-Diamonds and Y went 5 -Diamonds on his six card suit, going game. 4 852 v Q9 * J6 0 Q95432 4 K o 94 Y 7 3 K8 732 A B q A J 0 54 9 8 4 4* KIo32 08 Z J6 AQJ6 V 6 * AQ75 0 A K o 7 A 4-4-4-I distribution and a major suit valued at not less than three probable trump tricks, such as Z has in the above hand, may often be used to advantage, to shift partner's response of three in case that falls in your weakest suit and provided you are able to bid only three in your own best suit. Such 208 CORRECT CONTRACT BRIDGE procedure might be employed to advantage whether Y were to have A's cards or those held by B. Suppose that A and Y were to exchange holdings: then Z's opening bid of 2-No Trumps would be shifted by his partner to 3-Hearts; instead of bidding 3-No Trumps with a single low card of partner's suit, Z could shift to 3-Spades, without increasing the contract. Of course Z's partner would bid 4-Spades, and a little slam would result. Were the holdings of B and Y to be exchanged, Z would again shift his partner's 3-Hearts to 3 -Spades; upon Z's signal that he held only a single heart and four cards of each remaining suit, Z's partner should shift to 4-Clubs (A 4-card suit headed by a high honor), which Z would raise to s-Clubs, possibly yielding a little slam. If partners make highly intelligent use of the 2 -No Trump approach, this species of contracting will ordinarily yield excellent results, without confusion of ideas. LAWS OF CONTRACT BRIDGE 1927 Adopted and Issued by THE WHIST CLUB 38 East 39 St., New York Adopted by The Racquet & Tennis Club, N. Y. The Knickerbocker Whist Club The American Auction The Tennis and Racquet Club, Boston The Racquet Club, Philadelphia The American Whist League The Cavendish Club Bridge League The Racquet Club, Chicago The Racquet Club, St. Louis Copyright, 1927, by Tnz WHIST CLUB, Nzw Yoxz. All Righit Reserved CONTENTS PAGE Foreword............................................................................ 213 Laws of Contract Bridge...................................................215 Players......................................................................... 215 Cards...................................... 215 Rank of Cards.-........ —.... -..... —.215 Rank of Suits in Drawing..........................................216 The Draw......................................................................216 Forming Tables...............................................................216 Members Leaving a Table......................................216 Players Leaving a Table..........................2I7 Drawing for Partners and Deal.........................27 The Shuffle...................................................................218 The Hand.....................................................218 The Cut................................................. 2I9 The Deal.. —..........................219 Cards Touched During Deal...............-................ New Deal (Compulsory)........................22 New Deal (Optional)...................................................22 The Contracting...................-.........221 Bid.........................................................................22 Rank of Bids...2...2.................. 22I Insufficient Bid...........................222 Impossible Bid................222 Bid or Double Out of Turn........................223 Pass.............................. 223 Pass Out of Turn.............................................. 224 Doubles and Redoubles..............................224 Illegal Declarations...................................225 Changing Declaration..................................................226 Cards Exposed During the Contracting.................226 The Contract................................................................227 The Dummy..............................227 Lead and Play................................................................228 Cards Exposed During Play......................................229 Penalty for Exposed Cards............................. 230 212 CORRECT CONTRACT BRIDGE PAGE Leads Out of Turn and Cards Played in Error.........230 Tricks.................................................................. 232 The Made Contract............ —........................233 Extra Tricks. ---......................234 Undertricks............. —........................ —.234 Refuse and Renounce ---........ --- -—........ ----.....234 The Revoke.................. ----........234 Revoke Avoided.-......... --- —-- ---------------—........ 235 Renounce Penalty.. - -.................236 Revoke Penalty -- -...........2...3..6....... 6 Time Limitation of Revoke Claim.- -................ 237 Claiming Tricks -................-...................237 Conceding Tricks.......................................238 Game. ---................. —..... ---............ 238 Vulnerable. ---....-......-...... —..........238 Rubber...-.- —...-..... —..........239 Honors........................................................... 239 Slams.............................................................240 Scoring.......-..................................240 Consultation and Selection of Penalties......................242 Information...................................................243 Ethics and Etiquette....................................................244 Goulashes..........................245 Index to the Laws.................................................. 246 FOREWORD For the benefit of the many players who have recently taken up Contract Bridge, the following explanation is made: Laws are not drafted to prevent dishonorable practices; that they cannot accomplish. Ostracism is the only adequate remedy. The real object of the laws is to define the correct procedure and to provide for the situations which occur when a player through carelessness gains an unintentional, but nevertheless an unfair advantage. Consequently, penalties when provided are moderated to a minimum consistent with justice. An offending player should earnestly desire to pay the full penalty and thus atone for his mistake. When this essential principle is thoroughly understood, penalties are paid graciously and cheerfully, improper claims are not presented, arguments are avoided, and the pleasure of the players is materially enhanced. 213 THE LAWS OF CONTRACT BRIDGE PLAY ERS I. The game of Contract Bridge is played by four persons: two play as partners against the other two, each pair constituting a side. CARDS 2. (a) Two packs of playing cards with different backs are used. (b) A correct pack contains fifty-two cards divided into four suits of thirteen cards, one card of each denomination to a suit. (c) A perfect pack is one in which no card is torn, soiled, or otherwise so marked that it may be identified from its back. (d) Any player may demand two new packs to replace correct and perfect packs, provided he do so at the end of a hand and before the ensuing cut. The opponents of the player demanding them shall have the choice of packs, unless the demand be made at the beginning of a rubber, in which case the dealer has the choice. RANK OF CARDS 3. The cards of a suit rank: Ace (highest), King, Queen, Jack, IO, 9, 8, 7, 6, 5, 4, 3, 2 (lowest). 215 2i6 CORRECT CONTRACT BRIDGE RANK OF SUITS IN DRAWING 4. In the draw, as between cards of equal rank, the suits rank: Spades (highest), Hearts, Diamonds, Clubs (lowest). High wins. THE DRAW 5. For the purposes of the draw, a shuffled pack shall be spread face down on the table. Each player draws by lifting a card from the spread pack and showing its face. If a player show more than one card, or one of the four cards at either end of the pack, it is a misdraw by that player and he must draw again. FORMING TABLES 6. (a) A complete table consists of six members. In forming a table, candidates who have not played rank first and in the order in which they entered the room. Candidates who have played, but are not members of an existing table, rank next. Candidates of equal standing decide priority by the draw; high wins. (b) Before the beginning of a rubber, a candidate may enter any incomplete table by announcing his desire to do so. Such announcements, in the order made, entitle candidates to places as vacancies occur. MEMBERS LEAVING A TABLE 7. If a member leave a table, he forfeits all his rights at said table, unless he leaves to make up a table that cannot be formed without him and, LAWS OF CONTRACT BRIDGE 217 when leaving, announces his intention of returning when his place at the new table can be filled: in which case his place at the table he left must be reserved for him. When a member leaves a table to make up a new table which cannot be formed without him, and does not claim the right to retain his membership in the old table, he shall be the last to draw out of the new table. When two members leave a table pursuant to this law, the law applies to both. PLAYERS LEAVING A TABLE 8. (a) A player leaving a table may, with the consent of the other three players, appoint a substitute to play in his absence. Such appointment becomes void upon return of said player, or upon conclusion of the rubber; in any case, the substitute, when released, regains all his previous rights. (b) A player who breaks up a table by withdrawing from a table of four at the end of a rubber; or who, after availing himself of the privileges of paragraph (a), fails to return before the end of the rubber, cannot claim entry elsewhere as against the other three players from that table. DRAWING FOR PARTNERS AND DEAL 9. (a) A table having been formed, the members draw. He who draws highest becomes the first dealer and has choice of packs and seats; he may consult his partner before choosing, but, having chosen, must abide by his decision. He who draws second highest is dealer's partner and sits opposite him. The third highest has choice of the two re 2i8 CORRECT CONTRACT BRIDGE maining seats; fourth highest takes the vacant one. The members, if any, who draw lower than fourth, remain members of the table but do not play in the current rubber. (b) If, at the end of a rubber, a table consist of five or six members, those who have played the greatest number of consecutive rubbers are the first to lose their places as players, but do not lose their standing as members. The draw decides between players of equal standing. (c) At the beginning of every rubber, the players draw for partners and for choice of seats and packs. THE S H U FF LE IO. (a) After the players are seated at the beginning of a rubber, the player on the dealer's left shuffles the pack which 'dealer has chosen. All players have the right to shuffle, dealer having the right to shuffle last. (b) During each deal the still pack is shuffled by dealer's partner, who then places it face down at his right (at the left of the next dealer). (c) The pack must be shuffled thoroughly in view of all the players, but not so as to expose the face of any card. (d) If any provision of this law be violated, any player, before the deal starts, may demand a new shuffle. THE HAND i i. A hand begins with the cut and ends when the last card is played to the thirteenth trick; or when any or all of the remaining tricks have been conceded by either side. LAWS OF CONTRACT BRIDGE 219 THE CUT 12. (a) Dealer, immediately before the deal, places the pack before his right hand opponent, who lifts off the top portion and places it beside the bottom portion toward dealer, who then places the bot. tom portion on top. This constitutes the cut. (b) If the cut leave fewer than four cards in the top or bottom portion; or any card be faced or displaced; or there be any doubt as to where the pack was divided, or as to which was the top and which the bottom portion; or any but the proper player cut; or any but dealer complete the cut; or any player shuffle after the cut; a new shuffle and a new cut may be demanded by any player. THE DEAL I3. (a) The deal begins after the cut, and ends when the last card has been placed in turn in front of the dealer. The dealer distributes the cards one at a time, face down; the first card to the player on his left, and so on until all fifty-two cards are dealt, the last one to dealer. (b) Except at the beginning of a rubber, and except as in Laws 14, I5 and i6, the player to deal is the one on the left of the last previous dealer. CARDS TOUCHED DURING DEAL 14. If any player, except dealer, touch a card during the deal and thereby cause a card to be faced, making a new deal compulsory, the side opposed to the offender may add fifty points to its honor score. 220 CORRECT CONTRACT BRIDGE NEW DEAL (Compulsory) IS. I. There must be a new deal by the same dealer with the same pack: (a) If the cards be not dealt to the proper players into four distinct packets of thirteen cards each. (b) If, during the deal, any card be found faced in the pack, or be exposed on, above, or below the table. (c) If, before play begins, it be discovered that more than thirteen cards were dealt to any player. (d) If, during the hand, one player hold more than the proper number of cards and another less. II. There must be a new deal by the same dealer with a correct pack if, during the hand, the pack be proved incorrect. The current hand is void, but all previous scores stand. The pack is not incorrect on account of a missing card if found in the still pack, among the tricks, below the table, or in any place which makes it possible that such card was part of the pack during the deal. Any player may search for it; if it be not found, there must be a new deal by the same dealer with a correct pack. NEW DEAL (Optional) i 6. During the deal, any player who has not looked at any of his cards may demand a new deal: (a) If the wrong player deal; if the dealer omit the cut, or deal with the wrong pack. (b) If the pack be imperfect. In (a), the new deal is by the proper dealer with LAWS OF CONTRACT BRIDGE 221 his own pack; in (b), by the same dealer with a perfect pack. If no legal demand for a new deal be made under this law before the end of the deal, it stands and the player on the left deals next with the still pack. THE CONTRACTING I7. (a) The contracting begins when the deal ends, and ends when all four players pass; or after a declaration that three players in proper succession have passed. The first legal act of the contracting is a bid or pass by the dealer. Thereafter, each player in turn to the left must pass; bid, if no bid have been made; make a higher bid, if a bid have been made previously; double the last bid made by an opponent, or redouble an opponent's double, provided no bid has intervened. Each pass, bid, double or redouble is a declaration. (b) When all four players pass, no bid having been made, the hand is abandoned and the next dealer deals the still pack. BID 18. A bid is made by specifying any number from one (I) to seven (7) inclusive, together with the name of a suit or No Trump, thereby offering to contract that with such suit as trump, or with No Trump, the bidder will win at least the specified number of tricks over six. RANK OF BIDS I9. A bid of a greater number of tricks ranks higher than a bid of a less number. When two bids are of the same number, they rank: No Trump 222 CORRECT CONTRACT BRIDGE (highest), Spades, Hearts, Diamonds, Clubs (lowest). INS U F FIC IENT B ID 20. (a) A bid, unless it be the first bid of the hand, is insufficient if it be not higher than the last previous bid. (b) A player having made an insufficient bid, may correct it without penalty if he do so before another player has called attention to the insufficiency, or has declared; in which case an insufficient suit-bid must be made sufficient in the same suit; an insufficient No Trump bid, in No Trump. (c) If the player on the left of the insufficient bidder declare before attention has been called to the insufficiency, the insufficient bid stands and is treated as if sufficient. (d) If any player, other than the insufficient bidder, call attention to the insufficiency before the insufficient bidder has corrected his bid and before the next player has declared, the bidder must make his bid sufficient and his partner is barred from further participation in the contracting. In such case, the bid may be made sufficient by substituting any higher bid in any suit or No Trump. IMPOSSIB LE B ID 21. If a player bid more than seven, the bid is void, the offender and his partner are barred from further participation in the contracting, and either opponent may: (a) Demand a new deal. (b) Require the declaration to be played by the offending side at seven (undoubled or doubled). LAWS OF CONTRACT BRIDGE 223 (c) Direct that the contracting revert to the last legitimate declaration and be continued by the side not in error. BID OR DOUBLE OUT OF TURN 22. An out-of-turn bid is void, unless the opponent on the left of the offender declares before either the in-turn bidder declares, or before any player calls attention to the offense. When the out-of-turn bid is void, the contracting proceeds from the declaration of the proper bidder, and the partner of the offender is barred from further participation in the contracting; but the offender may declare thereafter in his proper turn. When the partner of the offender is the in-turn bidder, such turn passes to the next bidder. When the opponent on the left declares before the in-turn bidder, and before attention is called to the out-of-turn bid, the contracting continues from that declaration and there is no penalty. A double or redouble out of turn is subject to the same provisions and penalties as a bid out of turn, except when it is the partner's turn to declare, for which Law 26-g provides. PASS 23. When, in his proper turn in the contracting, a player does not bid, double or redouble, he must pass; he should do so by saying "Pass" or "No Bid," and the turn to declare is thereby transferred to the next player on the left, unless such pass ends the contracting. 224 CORRECT CONTRACT BRIDGE PASS OUT OF TURN 24. (a) If no bid have been made: A pass out of turn is void; the proper player declares, and the offender may not bid, double or redouble until the first bid has been overbid or doubled. (b) If a bid have been made: A pass out of turn is void; the proper player declares, and the offender may not bid or double until the declaration he passed is overbid or doubled. In either (a) or (b): if the player at the left of the offender declare before attention is called to the offense, the pass becomes regular, the contracting proceeds, and the offender may declare in turn. In either (a) or (b): if it be the turn to declare of the player on the right of the offender, a declaration by the in-turn player made before his partner declares, is regular and calls attention to the offense. DOUBLES AND REDOUBLES 25. During the contracting and in proper turn, a player may double the last previous bid, if made by an opponent, or redouble an opponent's double. Doubles and redoubles increase the values of made contracts (Law 36-b), extra tricks and undertricks (Law 52-b). Doubling or redoubling does not change bidding values (Law iv), the values of honors or slams, nor that part of a revoke penalty which is scored in points. A bid which has been redoubled may not again be doubled or redoubled. A double of an opponent's double is a redouble; a redouble of an opponent's bid is a double. LAWS OF CONTRACT BRIDGE 225 ILLEGAL DECLARATIONS 26. (a) A double or redouble, made before a bid has been made, is a double or redouble out of turn, for which Law 22 provides the penalty. (b) If a player bid, double or redouble, when barred from so doing, either opponent may decide whether or not such bid, double or redouble shall stand; and in any such case, both the offending player and his partner must thereafter pass. (c) A bid, double or redouble, made after the contracting is ended, is void. It is not penalized if made by Declarer or his partner, but if made by an adversary, Declarer may call a lead from the partned of the offender the first time it is the turn of said partner to lead. (d) A pass made after the contracting is ended, is void; no penalty. (e) A double or redouble of a redouble is void, and either opponent of the offender may demand a new deal, or add two hundred points to the honor score of his side. (f) A double of a partner's bid, or a redouble of a partner's double is void. Penalty: the opposing side may add one hundred points to its honor score. (g) If a player double or redouble when it is his partner's turn to declare, the opponents may consult before declaring further, and elect: (I) To call the bid made before the offense the final bid. (2) To call the doubled or redoubled bid the final bid. (3) To demand a new deal. (h) A player is not required to name the bid he 226 CORRECT CONTRACT BRIDGE is doubling or redoubling, but if he do so and name any bid other than the one he might legally double or redouble, his declaration is void; he must declare again, and his partner is barred from further participation in the contracting. CHANGING DECLARATION 27. A player who inadvertently says "No Bid" when meaning to say "No Trump," or vice versa; or who inadvertently names one suit when meaning to name another, may correct his mistake before the next player declares. A change in the number of tricks bid (except to make a bid sufficient), or from Pass to any bid, may not be made. By "inadvertently" is meant a slip of the tongue, not a change of mind. Except as above provided, a; player may not change his declaration: and if he attempt to do so, the second declaration is void and may be penalized as a bid out of turn. CARDS EXPOSED DURING THE CONTRACTING 28. If, during the contracting, a player lead or expose a card, it must be left face up on the table: and if it be a Ten or higher card, the partner of the offender is barred from further participation in the contracting. If the offender become Declarer or Dummy, the card is no longer exposed; but if the offender become an adversary, the card, regardless of its rank, remains exposed until played. LAWS OF CONTRACT BRIDGE 227 If the player at the left of the offender become Declarer he may, before the Dummy is exposed, prohibit a lead of the suit of the exposed card by the partner of the offender. When two or more cards are exposed by the same player, all are subject to the provisions of this law; but the Declarer may not forbid the lead of more than three suits. THE CONTRACT 29. At the end of the contracting the highest bid becomes the contract. The partners who secure the contract undertake to win at least six tricks (the book), plus the number of tricks named in the contract. The partners who secure the contract become respectively Declarer and Dummy. The player who first, for his side, named the suit or No Trump of the contract, becomes Declarer; his partner, Dummy. The partners who do not secure the contract become the adversaries: the- one on Declarer's left hereinafter termed Senior; the one on Declarer's right hereinafter termed Junior. THE DUMMY 30. (a) After the end of the contracting, unless all four players have passed initially, the play begins, and continues until the last card is played to the thirteenth trick. Senior leads; Dummy places his cards face up on the table and Declarer plays Dummy's cards in addition to playing his own. (b) During the play, Dummy may not: 228 CORRECT CONTRACT BRIDGE (i) Warn Declarer that he is about to lead from the wrong hand, nor tell him which hand has the lead. Penalty: either adversary may name the hand from which the lead shall be made. (2) Suggest a lead or play by touching or naming a card, or otherwise. Penalty: either adversary may direct that Declarer make such lead or play such card (if legal) or refrain from doing so. (c) Except as provided in (b), Dummy has all the rights of a player, unless he intentionally sees the face of a card held by Declarer or either adversary. (d) If Dummy have intentionally seen any such card, he may not call Declarer's attention to: (i) Any legal right. Penalty: forfeiture of such right. (2) A card exposed by an adversary. Penalty: the card is no longer exposed. (3) An adverse lead out of turn. Penalty: the adversaries, after consultation, may decide which of them shall lead. (4) An adverse revoke. Penalty: the revoke may not be claimed. (5) The fact that he has refused a suit by asking whether he have any or none of it. Penalty: Declarer may not change his play and is liable for any revoke resulting therefrom. LEAD AND PLAY 3I. When a player places a card face up on the table, his act is a play. The first play to a trick is a lead. LAWS OF CONTRACT BRIDGE 229 A lead or play is completed: (a) By an adversary, when the card is so placed or held that his partner sees its face. (b) By Declarer, when the card is quitted face up on the table. (c) By Dummy, when Declarer touches or names the card. If, in touching a card, Declarer say "I arrange," or words to that effect; or if he manifestly be pushing one or more cards aside to reach the one desired, touching the card does not constitute a lead or play. CARDS EXPOSED DURING PLAY 32. During the play the following are exposed cards: (a) When two or more cards are led or played simultaneously, the offender may designate which one is led or played, and the pthers are exposed, except any one so covered that its face is completely concealed. (b) A card dropped face upward on the table, even if picked up so quickly that it cannot be named. (c) A card dropped elsewhere than on the table, if the partner sees its face. (d) A card so held by a player that his partner sees any portion of its face. (e) A card mentioned by either adversary as being in his own or in his partner's hand. 230 CORRECT CONTRACT BRIDGE (f) If an adversary who has played to the twelfth trick, shows his thirteenth card before his partner plays his twelfth, the partner's two cards are exposed. (g) If an adversary throw his cards face up on the table, they are exposed, unless such act follows a claim by Declarer of a certain number, or the rest of the tricks. (h) A card designated by any law as "exposed." PENALTY FOR EXPOSED CARDS 33. (a) There is no penalty for a card exposed by Declarer or Dummy. (b) A card exposed by an adversary must be left face up on the table and Declarer may call it (i. e., require its owner to lead or play it) whenever it is the owner's turn to lead or play, unless playing it would cause a renounce. (c) Declarer may not prohibit the lead or play of an exposed card, and its owner may lead or play it whenever he legally can do so: but until played, Declarer may call it any number of times. LEADS OUT OF TURN AND CARDS PLAYED IN ERROR 34. (a) After the contracting ends and before Senior leads, should Junior lead or expose a card, Declarer may treat it as exposed, or require Senior (the proper leader) to lead a card of a suit named by Declarer. Dummy may call attention to the offense; but should Declarer and Dummy consult regarding the penalty, it is canceled. Should Dummy LAWS OF CONTRACT BRIDGE 23I show any of his cards before the penalty is selected, Declarer may call the exposed card, but may not call a lead. If an adversary lead out of turn during the play, Declarer may call the lead of a suit as soon as it is the turn of either adversary to lead, or may treat the card so led as exposed. (b) Should the adversaries lead simultaneously, the correct lead stands and the other is an exposed card. (c) Should Declarer lead out of turn either from his own hand or Dummy, such lead shall stand, unless an adversary call attention to the error before he or his partner plays. When attention is called to the error in time, Declarer must lead from the proper hand; and, if that hand have a card of the suit led from the wrong hand, he must lead that suit. (d) Should any player (including Dummy) lead out of turn, and next hand play, the lead stands as regular. If an adversary lead out of turn, and Declarer play next, either from his own hand or Dummy, the adverse lead stands as regular. (e) Should an adversary who has played a card which is a winner as against Declarer and Dummy, lead another or several such winning cards without waiting for his partner 'to play, Declarer may require said adversary's partner to win, if he can, the first or any of these tricks, after which the remaining card or cards thus led are exposed. (f) After a lead by Declarer or Dummy, should Fourth player play before Second, Declarer may require Second player to play his highest or lowest card of the suit led, or to win or lose the trick. If 232 CORRECT CONTRACT BRIDGE he have none of the suit led, Declarer may call his highest of any designated suit; if he hold none of the suit called, the penalty is paid. (g) Should Declarer lead from his own hand or Dummy, and play from the other hand before either adversary plays, either adversary may play before the other without penalty. (h) If a player (not Dummy) omit playing to a trick and then play to a subsequent trick, Declarer or either adversary (as the case may be) may demand a new deal whenever the error is discovered. If no new deal be demanded, the surplus card at the end of the hand is considered played to the imperfect trick, but does not constitute a revoke therein. (j) Whenever it is suspected that any of the quitted tricks contain more than four cards, any player may count them face downward. If any be found to contain a surplus card, and any player be short, either opponent of the player who is short may face the trick, select the surplus card, and restore it to the player who is short; but this does not change the ownership of the trick. The player who was short is answerable for any revoke as if the missing card had been in his hand continuously. Should the side in whose tricks the surplus card is found, have failed to keep its tricks properly segregated, either opponent of such side may select a card from the tricks improperly gathered and restore such card to the player who is short. TRICKS 35. (a) Unless compelled, as a penalty, to lead in a certain way, a player may lead any card he holds; after each lead, each player in turn to the LAWS OF CONTRACT BRIDGE 233 left must follow suit if he can. A player having none of the suit led, may play any card he holds. (b) A trick consists of four cards played in succession, beginning with a lead. (c) A trick containing one trump-card or more, is won by the player who plays the highest trumpcard. A trick containing no trump-card, is won by the player who plays the highest card of the suit led. (d) Declarer gathers all tricks won by himself or Dummy; either adversary may gather all tricks won by his side. All tricks gathered by a side should be kept together and so arranged that the number thereof may be observed, and the identity of each trick readily established. A trick gathered by the wrong side may be claimed by the rightful owners at any time prior to recording the score for the current hand. (e) A quitted trick may be examined upon demand of any player whose side has not led or played to the following trick. (f) The winner of each trick leads to the next, until the last trick is played. THE MADE CONTRACT 36 (a) The Made Contract represents the number of tricks won by Declarer after he has won six tricks, up to and including the number of tricks named in his contract. The first six tricks won by Declarer constitute his book and have no scoring value. If Declarer fails to win the contract, his side scores nothing for tricks; but if he makes his contract, his side scores in their contract score, the value, normal, doubled or redoubled, of the Made Contract. For the Made Contract trick values see 234 CORRECT CONTRACT BRIDGE Law 52-a. The value normal, doubled or redoubled of their Made Contract is the only score either side can score in its contract score. All other points, including extra tricks made, are scored in the honor score. (b) Doubling doubles the normal value of the tricks of the Made Contract; redoubling multiplies by four the normal value of said tricks. EXTRA TRICKS 37. (a) Extra tricks are tricks won by Declarer in excess of his Made Contract. (b) Extra tricks are scored in the honor score (Law 52-b). UNDERTRICKS 38. (a) The book of the adversaries is seven minus the number of tricks named in Declarer's contract. When the adversaries win a trick or tricks in addition to their book, such tricks are undertricks. (b) The adversaries score in their honor score for all undertricks (Law 52-b). REFUSE AND RENOUNCE 39. To fail to follow suit is to refuse: to refuse when able to follow suit is to renounce. THE REVOKE 40. (a) A renounce becomes a revoke: (i) When a renouncing player or his partner, whether in turn or otherwise, leads or plays to the following trick. LAWS OF CONTRACT BRIDGE 235 (2) When the renouncing player or his partner claims the remaining tricks, or any of them. (b) When one side claims a revoke, if either opponent mix the cards before the claimant has had reasonable opportunity to examine them, the revoke is established. (c) When a player has incurred a penalty requiring him to play the highest or lowest of a suit, or to win or lose a trick, or to lead a certain suit, or to refrain from playing a certain suit; and fails to act as directed when able to do so: he is subject to the penalty for a revoke. (d) When any player (except Dummy) is found to have less than his correct number of cards, and the other three have their correct number, the missing card or cards, if found, belong to the player who is short and he is answerable for any revoke or revokes as if said card or cards had been in his hand continuously. REVOKE AVOIDED 41. A renouncing player is not penalized for revoke under the following circumstances: (a) A renounce by Dummy must be corrected if discovered before the lead to the next trick. After such lead, the renounce may not be corrected. There is no penalty in either case. (b) Should Dummy leave the table, Declarer cannot be penalized for revoke, unless an adversary call the renounce to his attention in time to enable him to correct it. (c) When a player refuses, any other player may ask whether he has any or none of the suit led; and 236 CORRECT CONTRACT BRIDGE if he admit that he has renounced before his renounce has become a revoke, he shall be subject to the penalty for a renounce, but not to the penalty for a revoke. Dummy may not ask the above question, if he have intentionally seen a card of another player. RENOUNCE PENALTY 42. A renounce made by any player (except Dummy) may be corrected by such player at any time before he or his partner has led or played to the following trick, or claimed any of the remaining tricks. In that case there is no revoke penalty; but the player, if an adversary, may be required to play his highest or lowest card of the suit led. Declarer, instead of calling the highest or lowest, may treat the card played in error as exposed. A Declarer who has renounced may be required by either adversary to play his highest or lowest, if the adversary on his left have played after the renounce. Any player who has played after a renounce may, if it be corrected, withdraw his card and, without penalty, substitute another; if an opponent have led to the next trick, that lead may be changed. REVOKE PENALTY 43 (a) Two tricks for the first revoke by any player. (b) One hundred points penalty scored in adversaries' honor score for each subsequent revoke. Penalty tricks are taken at the end of the hand from the tricks of the revoking side and added to the tricks of the other side. They count exactly as if won in play and assist Declarer to make his con LAWS OF CONTRACT BRIDGE 237 tract or to go game; or may assist the adversaries to defeat the contract, in which case they carry full penalty values. If they make the total twelve or thirteen tricks for Declarer, they carry the proper slam premium if bid. If the contract be doubled or redoubled, they count at the doubled or redoubled value in the contract score of the Declarer, and carry their full premium or penalty values in the honor score of either side. After surrendering these tricks, the revoking side may score for its remaining tricks as it would if it had not revoked. If the revoking side have not enough tricks to pay the penalty in full, the adversaries take all the tricks they have and 1oo additional points in their honor score for each revoke which would otherwise remain in whole or in part unpenalized. TIME LIMITATION OF REVOKE CLAIM 44. No revoke penalty may be claimed after the next ensuing cut; nor, if the revoke occur during the last hand of the rubber, after the score has been agreed upon; nor, if there have been a draw for any purpose in connection with the next rubber. CLAIMING TRICKS 45. If Declarer claim the remaining tricks or any number thereof, either adversary may require him to place his cards face up on the table and to play out the hand. In that case, Declarer may not call any cards either adversary has exposed, nor refuse to trump a doubtful trick when able to do so, nor take any finesse unless: 238 CORRECT CONTRACT BRIDGE (a) He announces his intention to do so when making his claim; or (b) The adversary on the left of the finessing hand had refused the suit before the claim was made. CONCEDING TRICKS 46 (a) Declarer may concede one or more tricks unless Dummy promptly objects; but if Dummy have intentionally seen a card in the hand of a player, he may not object. If, after a concession by Declarer and before objection by Dummy, an adversary face his cards, they are not exposed. (b) Either adversary may concede one or more tricks to Declarer, unless the other adversary promptly objects; but if the conceding adversary face his cards, they are exposed. GAME 47. A game is won when one side makes a contract score of Ioo or more points. A game may be completed in one hand or more; each hand is played out and the full value of a made contract is counted, whether or not needed to make game. No contract points are carried over from one game to the next; each side starts a new game with a contract score of zero. VULNERABLE 48. After a side wins one game it becomes "Vulnerable." Until a side wins a game it is "Not Vulnerable." LAWS OF CONTRACT BRIDGE 239 R U B B E R 49. (a) A rubber begins with the draw and is completed when one side has won two games; when one side wins the first two games, the third game is not played. The side having the net points (Law 5 2-C) wins the rubber. (b) When a rubber is started with the agreement that the play shall terminate (i. e., no new hand shall commence) after a specified time, and the rubber is unfinished at that time, the score is made up as it stands, two hundred points being added to the honor score of the winners of a game. A hand, if started, must be played out; but if a player refuse to finish it, his opponents may elect whether it be thrown out or c6unted at their estimate of the probable result. (c) If a rubber be started without any agreement as to its termination, and before its conclusion one player leave; or if, after an agreement a player leave before the specified time, and in either case fail to appoint an acceptable substitute, the opponents have the right to consult and decide whether the score of the unfinished rubber be canceled or counted as in (b). H O N O R S 50. (a) In a No-Trump Contract, the honors are the four aces; in a suit contract, the honors are the Ace, King, Queen, Jack and Ten of that suit. (b) Honors are scored in the honor score of the side to which they are dealt; their value is not changed by doubling or redoubling. Honor premiums are additional to all other premiums (Law 52-b). 240 CORRECT CONTRACT BRIDGE SLAMS 51 (a) A Grand Slam is the winning of thirteen tricks by the Declarer. A Small Slam is the winning of twelve tricks by the Declarer. (See also Law 43-b). (b) Slam premiums are additional to all other premiums; and to score the premium, the slam must be contracted for. Their value is not changed by doubling or redoubling (Law 52-b). SCORING 52. (a) Contract Score: Each side has a contract score in which are recorded only points for Made Contracts. (Law 36.) Each Made Contract counts per trick: With No Trump............................. 35 points W ith Spades Trumps...................................... 30 points With Hearts Trumps.-.. —........-. —......3- 30 points W ith Diamonds Trumps...................................... 20 points With Clubs Trumps............................... 20 points Doubling and Redoubling, Law 36-b. Rank of Bids, Law I9. (b) Honor Score: Each side has an honor score in which all premiums and all penalties are scored as follows: PREMIUMS Honors: Points 4 Trump Honors in one hand................................ oo 5 Trump Honors in one hand............................. 50 4 Aces in one hand in No Trumps —.1...... —....... 50 All Other................................. None For Winning Final Game of Rubber: If a two-game rubber............................................... 700 If a three-game rubber..-.. —............... —..... 500 LAWS OF CONTRACT BRIDGE 241 Making Contract: Points If Undoubled....................................................... None If Doubled (When Declarer is Not Vulnerable)...... 50 (When Declarer is Vulnerable)............ oo Extra Tricks: If Undoubled (When Declarer is Vulnerable or Not Vulnerable), per trick.................................. 50 If Doubled (When Declarer is Not Vulnerable), per trick................................................................. (When Declarer is Vulnerable), per trick.... 200 Slams Bid and Made (Law 51): Little Slam (When Declarer is Not Vulnerable)...... 500 (When Declarer is Vulnerable)............. 750 Grand Slam (When Declarer is Not Vulnerable)...iooo (When Declarer is Vulnerable)...................500 Unbid Slams Made................................No Slam premiums PENALTIES Undertricks (Scored in Adversaries' honor score): If Undoubled (When Declarer is Not Vulnerable) per trick................................... 50 If Undoubled (When Declarer is Vulnerable) for first trick................................... Ioo for subsequent tricks........................ 200 If Doubled (When Declarer is Not Vulnerable) first two tricks, per trick................. 0oo for third and fourth tricks, per trick 200 for subsequent tricks, per trick........ 400 If Doubled (When Declarer is Vulnerable) for the first trick.............................. 200 for subsequent tricks, per trick.......... 400 Redoubling doubles the doubled premiums and penalties. Neither doubling nor redoubling changes the premiums for games, slams and honors; nor the penalty in the honor score for the revoke. (c) At the end of the rubber, the total points of a side are obtained by adding together its contract 242 CORRECT CONTRACT BRIDGE score and its honor score. Subtracting the smaller total from the greater gives the net points by which the rubber is won and lost. (d) A proved error in the honor score may be corrected at any time before the score of the rubber has been made up and agreed upon. (e) A proved error in the contract score may be corrected at any time before the next contracting begins; or, if the error occur in the final hand of the rubber, before the score has been made up and agreed upon. (f) A proved error in addition or subtraction may be corrected whenever discovered. C O N S U L T A T I O N A N D S E L E C T I O N OF PENALTIES 53. Laws that give "either partner," "either opponent," etc., the right to exact a penalty do not permit consultation. (a) If either partner suggest or name a penalty, he is deemed to have selected it. (b) If either direct the other to select a penalty, the latter must do so; and, if an attempt be made to refer the privilege back, the penalty is canceled. (c) If either say (in effect): "Which of us is to select the penalty?" the penalty is canceled. (d) A proper penalty once selected may not be changed. (e) If a wrong penalty be selected, the selection must be corrected upon request of either opponent. (f ) If a wrong penalty be selected and paid without challenge, the selection may not be changed. (g) A reasonable time must be allowed for the selection of a penalty. (h) If, instead of exacting a penalty at the LAWS OF CONTRACT BRIDGE 243 proper time, either opponent of the side in error declare or play, no penalty may be exacted. INFOR MATION 54. (a) During the contracting, information must be given concerning its details; but, after it is ended, should either adversary or Dummy inform his partner regarding any detail of the contracting, except the contract, Declarer or either adversary (as the case may be) may call a lead the next time it is the turn of the offending side to lead. At any time during the play, any player inquiring must be told the final bid, and whether it was doubled or redoubled; but no information may be given as to who doubled or redoubled. (b) Any player (except Dummy) may, before a trick is turned and quitted, demand that the cards so far played be indicated by their respective players; but should either adversary, in the absence of such demand, in any way call attention to his own card or to the trick, Declarer may require the partner of the offender to play his highest or lowest card of the suit led, or to win or lose the trick. (c) Either adversary, but not Dummy, may call his partner's attention to the fact that he is about to play or lead out of turn; but if, during the play, an adversary make any unauthorized reference to any incident thereof, or to the location of any card, Declarer may call a lead when it next becomes an adversary's turn to lead. Any such reference by Dummy may be similarly penalized by either adversary. (d) If, before or during the contracting, a player give any unauthorized information concerning his 244 CORRECT CONTRACT BRIDGE hand, his partner may be barred from further participation in the contracting. ETHICS AND ETIQUETTE Offenses against the ethics and etiquette of the game are unpardonable, as they are not subject to prescribed penalties. The only redress is to cease playing with those who habitually disregard the following: I. 'Declarations should be made simply, without emphasis, and without undue delay. 2. A player who has looked at his cards, should not indicate by word, manner, or gesture, the nature of his hand; nor his approval or disapproval of a bid, double or play; nor call attention to the score. 3. A player should not allow any hesitation or mannerism of his partner to influence his own declaration or play. 4. If a player demand that the bidding be reviewed, or that the cards played to a trick be indicated, he should do so for his own information and not to call his partner's attention to any bid or play. 5. An adversary should not lead until the preceding trick has been gathered; nor, having led a winning card, should he draw another from his hand before his partner has played to the current trick. 6. A card should not be played with emphasis, nor in such manner as to draw attention to it; nor should a player detach one card from his hand and subsequently play another. 7. No player should hesitate unnecessarily in his play, in order to create a wrong impression regarding his hand. 8. Dummy should not leave his seat to watch Declarer play. LAWS OF CONTRACT BRIDGE 245 9. Except when permitted by law, a player should not look at a trick that has been turned and quitted. IO. A player should not purposely incur a penalty, even though willing to pay it; nor make a second revoke to conceal a first. G O U L A S H E S (Optional) When all four players pass, no bid having been made, and the players desire to play a Goulash, the cards shall be redealt by the same dealer. Before surrendering his hand, each player shall sort his cards into suits, arranging the cards in each suit according to value (Law 3). The dealer then places his cards face down on the table, and each player in turn, beginning with the player on the right of the dealer, places his cards face down on top of those of the preceding player. The cards are then cut by the player at dealer's right (no shuffling of any kind permitted) and are dealt as follows: Five at a time to each player in turn, beginning with the player on the left of the dealer, again five at a time to each player, and finally three at a time to each player. When all four players pass, no bid having been made, the same procedure is followed as before, the cards being dealt by the same dealer. If a misdeal is properly called the goulash is abandoned and the next dealer deals in the regular way with the still pack. INDEX Ace high, 3. Adversary (ies). -'s book, 38(a). -calls attention to renounce, 41 (b) -completes lead or play, 3I (a). -concede tricks, 46 (b). — correct renounce, 42. -exposes cards, 30(d-2), 32(e), 32(9), 33(b), 34 --gathers tricks, 35 (d). -"-" is opponent of declarer, 29. -lead simultaneously, 34(b). -leads or plays out of turn, 34. -leads several winning cards, 34 (e) -mentions card, 32 (e). — s undertricks, 38. -shows I3th card, 32(f). -suggests "playing it out," 46(b). Addition, error in, 52 (f). Agreement to terminate rubber, 49 (b), 49(c). "Asking" about renounce, 30(d-5), 4I(b), 4 I (). Barred from contracting, 20(d), 21, 22, 24(a), 24(b), 26(a), 26(b), 26(h), 28, 54(d). Barred from play. See Compulsory plays. Bid. Changing-, 20(b), 2o(d), 27 "Declare" includes "-," 17 (a). -defined, 8. Higher -r- defined, I9. Impossible -, 2I. 246 LAWS OF CONTRACT BRIDGE 247 Insufficient —, 20. Irregular -, 20, 21, 22, 26, 27. -made after contracting ends, 26(c). -made when under compulsion to pass, 26(b). "no' -" changed to "no trump," 27. -of over seven, 21. -out of turn, 22. Rank of -s, 19. Book. Adversaries' -, 38 (a). Declarer's -, 29, 36(a). Breaking up a table, 8. Calling card, lead, highest, lowest, ctc. See Compulsory plays. Cancelling score, 49 (b), 49 (c). Candidates, 6. Card(s). See also Pack(s). Adversary leads several winning -, 34 (e). Backs of -must be different, 2 (a). Calling -, see Compulsory plays. - dealt into four packets, 15(a). Declarer plays Dummy's -, 30(a). - displaced in the cut, 12 (b). Drawing -, 5, 6(a), 9(c). -dropped 5 II, 32 (b), 32 (c). -exposed, see Exposed cards. faced -, see Exposed cards. Four- in cut, 12 (b). Four -in draw, 5. -improperly dealt, IS, I6. Laying down -, 30(a), 32(g), 45, 46. — led or played simultaneously, 32(a), 34(b). Looking at -, 14, I6. Marked -, 2(c). -mentioned by adversary, 32 (e). 248 CORRECT CONTRACT BRIDGE Missing, 15 II, 34(j), 40(d). Mixing the - when revoke is claimed, 40(b). New-, 2(d). Placing-, 54(b). -played in error, 34. Player holds too few or too many -, I5(c), I5(d). Quitted trick contains too many or too few-, 34(h), 34(j)Rank of-, 3. Shuffling -, Io. Soiled -, 2(c). Torn -, 2(c). -touched by declarer, 31 (c). -touched by dummy, 30 (b-2). -touched during deal, 14. Touching -, 14, 3o(b-2), 31 (c). Two packs of-used, 2 (a). -withdrawn following renounce, 42. Changing declaration, 27. Choice of packs and seats, 2 (d), 9. Claiming "the rest," 40(a-2), 45. Clubs count twenty, 52(a). Complete table, 6 (a). Completed lead a play, 31. Compulsory plays, 26(c), 28, 3o(b), 30(d-2), 32(a), 33, 34(a), 34(c), 34(e), 34(f), 40(c), 42, 45, 46(a), 54(a), 54(b), 54(c). Conceding tricks, 46. Consultation, 9(a), 26(g),30(d-3), 34(a), 49(b), 49(c), 53. Contract. -Bridge, I. -defined, 29. Failing to make -, 36 (a). LAWS OF CONTRACT BRIDGE 249 Giving information regarding -, 54(a). Highest bid becomes -, 29. -lost by revoke, 43 (b). Made -, 36. -score, 52. -won by revoke, 43 (b). Contracting. Barred from -, see Compulsory plays. -begins and ends, 17 (a). Three or four passes during -, 17 (a), 7 (b). Correct pack, 2(b), 15 II. Correcting scores, 52 (d), 52 (e), 52(f). "Courtesies of the table," 41 (b). Cut. completed by dealer, I2(a), I2(b). Deal begins after -, 13 (a). - described, 12. Improper-, 12(b). Must - four cards, 12 (b). -omitted, I6(a). Wrong player -s, I2(b). Cutting for deal and partners. See Draw(ing). Cutting out. See Draw(ing). Deal. -after cut, 3 (a). -by wrong dealer, i6(a). Cards touched in -, 14. Contracting begins after -, 7 (a). - described, 13. Drawing for -, 9. Irregular-, 14, 15, i6. Looking at cards during —, 4, 6. New -, see New deal. -out of turn (I6(a). "Passed out"-, 17 (b). 25~ CORRECT CONTRACT BRIDGE Players - in turn to left, 13 (b). When - begins and ends, I3(a). - with imperfect or incorrect pack, 15 II, i6(b). -with wrong pack, I6 (a) Dealer. -completes cut, 2(a), I (b). - deals improperly, 15, i6. First -, how selected, 9 (a). New-deals, I6(a), I7(b). - omits cut, 6 (a). -'s partner, 9(a). Same -deals, 15, 6 (b). -shuffles last, o (a). Declaration. See also Declare. -changed, 27. Inadvertent -, 27. Irregular -, 26. " —" includes "bid," "pass," "double," and "redouble," 17 (a). -made when under compulsion to pass, 26(b). Declaration out of turn. Bid after end of contracting, 26(c). Bid by barred player, 26(b). Double after end of contracting, 26(c). Double by barred player, 26(b). Double made before bid, 26(a). Irregular - condoned or penalized, 20, 21, 22, 24, 26. Pass after end of contracting, 26(d). Pass made before bid, 24(a). Redouble after end of contracting, 26 (c). Redouble by barred player, 26(b). Redouble made before bid, 26(a). Declare(s). See also Declaration. LAWS OF CONTRACT BRIDGE 251 -ing and changing, 27. "-" includes "bid," "pass," "double," and "redouble," 17(a). Declarer. "Adversary" is -'s opponent, 29. -and contract, 29, 36(a). - and dummy, 29. -'s, book, 29, 36(a). - claims or concedes tricks, 45, 46 (a). - completes lead or play, 3 I(b), 3 (c). -defined, 29. -gathers tricks, 35 (d). - leads from wrong hand, 34 (c). -leads out of turn, 34. -makes contract by adverse revoke, 43(b). -may not forbid lead of exposed card, 33(c). - may not forbid lead of more than three suits, 28. - not liable for exposed cards, 33 (a). Only - scores for tricks over six, 36 (a). -'s partner exposes hand, 30(a), 34(a). Partner who first names suit is -, 29. -plays dummy's cards, 30(a). -plays out of turn, 34(c), 34(g). - taking finesse, 45. - touching card, 31(c). Definitions. Adversary, 29. Bid, I8. Bid out of turn, 22. Book, 36 (a), 38 (a). Contract, 29. Contract Bridge, I. Contract Score, 52(a). Contracting, 17. Correct pack, 2. Cut, 12. Deal, I3. Declaration, 17(a). Declare, 17(a). Dedarer, 29. Double, 25. Drawing, 9. Dummy, 29. Exposed cards, 32. Extra tricks, 37. Following suit, 35(a). Game, 47. Hand, iI. 252 CORRECT CONTRACT BRIDGE Higher bid, 19. Honor score, 52 (b). Honors, 50(a). Imperfect pack, 2. Impossible bid, 21. Insufficient bid, 20. Lead, 31. Member, 6. Net points, 52 (c). Odd tricks, 36 (a). Partners, i. Pass, 23. Play, 31. Premiums, 52(b). Redouble, 25. Refuse, 39. Renounce, 39. Revoke, 40. Rubber, 49(a). Shuffle, Io. Side, I. Slam, 5I. Total points, 52(c). Trick, 35(b). Tricks over six, 36(a). Undertrick, 38. Vulnerable, 48. Winning rubber, 49(a). Demanding new cards, 2(d). Deuce low, 3. Diamonds count twenty, 52(a). Double. -after contracting ends, 26 (c). -before a bid is made, 26(a). "Declare" includes "-," I7(a). -defined, 25. -does not change bidding values, etc., 25, so (b). -increases trick values, etc., 25, 36(b), 52(b). -of a -, 25. -of designated suit, 26 (h). - of partner's bid, 26 (f). -of redouble, 26 (e). -out of turn, 22, 26(a), 26(g). - when turn of partner, 26(g). - when under compulsion to pass, 26 (b). Draw(ing). All - from same pack, 5. -for cutting out, 9(b). -for deal, 9(a). -for entry, 6(a). - for packs and seats, 9. -for partners, 9(a), 9 (c). LAWS OF CONTRACT BRIDGE 253 -, how conducted, 5. -more than one card, 5. Rank of cards in -, 3. Rank of suits in -, 4. Dummy. -completes lead or play, 31(c). - corrects renounce, 41 (a) Declarer plays -'s cards, 30 (a). -defined, 29. -exposes cards prematurely, 34(a). -leads out of turn, 34(c). -leaving table, 41 (b). -'s limitations (conditional), 30(d), 4I(c), 46(a). -'s limitations (unconditional), 30(b). -not liable for exposed cards, 33 (a). -not liable for revoke, 4I (a). -'s rights, 30(c), 34(a). -suggests "playing it out," 46 (a). -touching cards, 30(b-2), 31(c). Entry at table, 6, 7, 8 (b). Error. Cards played in -, 34. -in addition and subtraction, 52(f). - in contract score, 52 (e). -in dealing, I5, i6. -in honor score, 52(d). Ethics and etiquette following law, 54. Exposed cards. -after claiming tricks, 45. -after conceding tricks, 46. - after renounce, 42. -by Junior, 34 (a). Calling -, see Compulsory plays. -cannot force renounce, 33 (b). 254 CORRECT CONTRACT BRIDGE Declarer and dummy not liable for -, 33 (a). - defined, 32. Dummy calls attention to -, 30(d-2). - during contracting, 28. -during cut, 2 (b). - during deal, I4, i (b). -during play, 32, 34 (e). -during shuffle, I o (c). Penalty for -, 33. -may be called several times, 33 (c). -may be played, 33 (c). Two or more-, 32(a), 32 (9), 34(b). Exposed ten, 28. Extra tricks, 37, 52 (b). Faced cards. See Exposed cards. Failing to play as directed, 40(c). Finesse, when not to be taken, 45. Following suit, 35 (a). Forming tables, 6. Fourth hand plays before second, 34(f). Game(s). All, points counted, 47. -, how played, i. Hundred points to a -, 47. - score, 52(b). - starts at zero, 47. Two - win rubber, 49 (a). -won by revoke, 43 (b). Gathering tricks, 35 (d). Giving information, 54. Goulashes, 39, 40. Grand slam, 5 (a), 52 (b). Hand. — begins and ends, I. Each - played out, 47. LAWS OF CONTRACT BRIDGE 255 Hearts count thirty, 52 (a). Higher bid. Bid, if not -, is insufficient, 20(a). -defined, I9. -must be made, 7 (a). Honor(s). -counts as dealt, So(b). described, 50 (a). — not affected by double or redouble, 50(b). -score, 36(a), 52(b). — values, 5o(b). "I arrange," 31(c). Imperfect pack. - causes new deal, 6 (b). -defined, 2(c). Impossible bid, 21. "Inadvertently" defined, 27, Incomplete table, 6(b). Incorrect pack. -causes new deal, 15 II. -defined, 2 (b). Information, 54.. Initial lead, 30(a). Insufficient bid. -condoned, 20(c). -corrected, 20 (b), 20 (d). -defined, 20 (a). - penalized, 20(d) Junior. -defined, 29. -leads out of turn, 34(a). Laying down cards, 30(a), 32(9), 45, 46, Lead. - by partner of proper leader, 34. Calling a -, see Compulsory plays. 256 CORRECT CONTRACT BRIDGE Changing -, 42. - completed by adversary, 31 (a). - completed by declarer, 3 (b). - completed by dummy, 31 (c). - defined, 3I. - establishes revoke, 40(a-I). - from wrong hand, 34. Initial - by Senior, 30(a). - of several winning cards, 34(e). -out of turn, 3o(b-I), 30(d-3), 34. - simultaneously, 34 (b). Which player -s, 30 (a), 35 (a), 35 (f) Leaving. - four cards in cut, I2(b). - four cards in draw, 5. -table, 7, 8, 41 (b), 49(b), 49(c). Looking at quitted trick, 15 II, 35(e), 40 (b). Losing trick (compulsory). See Compulsory plays. Made contract, 36, 52. Making up tables, 6. Marked cards, 2 (c). Members. - draw for partners and deal, 9 (a). - leaving tables, 7. -of table, 6(a), 7, 8. Six - make complete table, 6(a). Misdeal, 15, i6. Misdraw, 5. Missing cards, I5 II, 34(j), 40(d). Naming. -card, 30(b-2), 3I(c), 32(e). - doubled or redoubled bid, 26 (h). Net score, 49(a), 52(c). New. -cards, 2(d), I5 II, i6(b). LAWS OF CONTRACT BRIDGE 257 — cut, 12(b). - deal, see New deal. - shuffle, io(d), I2(b). New deal. Compulsory-, I5. - for card faced or exposed, 15 I (b). -for cut omitted, I6 (a). - for deal by wrong dealer, I6 (a). - for dealing with wrong pack, I6 (a). -for exposed card, 14, IS(b). - for illegal double or redouble, 26(e), 26 (g-3). -for imperfect pack, 6 (b). - for impossible bid, 21 (a). -for improper number of cards dealt, I5(a), IS(c), I5(d). -for incorrect pack, I5 II. -for irregular deal, 15, i6. -for missing cards, I5 II. - for omitting playing to trick, 34 (h). Optional-, I6. - when four players pass, 7 (b). "No Bid" (same as "Pass"). "-_" changed to "No Trump" or vice versa, 27. No trump. -defined, 18. - highest in contracting, 19. -honors, 50(a). - tricks count thirty-five, 52(a). Opponents call attention to renounce, 41 (b), 41 (c). Pack(s). See also Card(s). Backs of - must be different, 2(a). Choice of -, 9. Correct -, 2(b), 15 II. New-, 2(d), 15 II, I6(b). Perfect-, 2(c), I6(b). 258 CORRECT CONTRACT BRIDGE Replacing -, 2(d). Shuffling -, Io. Soiled -, 2(c). Still -, Io(b), I 5 II. Two -used, 2 (a). Wrong - dealt, I6 (a). Partners, I, 9. Pass. "Declare" includes -, 7 (a). - defined, 23. - ends contracting, 17, 23. Four players - in succession, I7 (a), 7 (b). - made after contracting ends, 26 (d). - ("no bid") changed to no trump, 27. -out of turn, 24, 26(d). Three players -, 7 (a). Penalty. Reasonable time for selecting -, 53 (g) Selection of -, 53. - score, 52(b). Penalty applied. Barred from contracting, 20(d), 21, 22, 24(a), 24(b), 26(a), 26(b), 26(h), 28, 54(d). Bidding errors, 22, 26. Breaking up tables, 8 (b), 49 (c). Calling exposed card, see Exposed cards. Calling or prohibiting card, lead, suit, highest or lowest, lose or win, etc., see Compulsory plays. Consultation, 53. Contract failure, 36(a). Cut omitted, I6 (a). Cutting wrong, 2 (b). Dealing errors, Is, i6. Declaration errors, 20, 21, 22, 24, 26, 27. LAWS OF CONTRACT BRIDGE 259 Doubling errors, 22, 26. Exposed cards, 33. Failure of play to trick, 34(h). Improper information, 54. Insufficient bid, 20(d). Lead out of turn, 30(d-3), 34(a). Leaving table, 8, 5i (c). Refusing to finish rubber, 54 (b). Renounce, 41 (c), 42. Revoke, 30(d-4), 30(d-5), 34(j), 40(c), 43. Shuffling errors, io(d). Undertricks, 52(b). Wrong number of cards held, 5 (c), 5 (d). Perfect pack, 2 (c). Placing cards, 54(b). Play. Barred -, see Compulsory plays. -begins and ends, 30 (a). completed by adversary, 31 (a). - completed by declarer, 31 (b). - completed by dummy, 31 (c). Compulsory -, see Compulsory plays. - defined, 3 I. -establishes revoke, 40(a-I). failing to - as directed, 40(c). -ing out of turn, 34. -ing out the hand, 45, 47, 49(b)< -ing to a trick, 35. Order of -, 35 (a). Player(s). Four - in game, I. - leaving table, 8. Playing cards, 2. Points. All game -counted, 47. 260 CORRECT CONTRACT BRIDGE, how scored, 52. - not carried forward, 47. One hundred - to game, 47. Premiums, 52(b). Priority. - among candidates, 6. - among members, 9. Protection from "revokes," 41(b). Quitted. -cards, 31. -tricks, 34(h), 34(j), 35(e), 54(b). Rank. -of bids, I9. -of cards, 3. - of players, 6, 7, 8. - of suits, 4. Redouble. -after contracting ends, 26 (c) -before a bid, 26(a). "Declare" includes "-," I7 (a) -defined, 25. -does not change bidding values, etc., 25, o (b).,-increases trick values, etc., 25, 36(b), 52(b). — of designated suit, 26 (h). -of opponent's bid, 25. -of partner's double, 26(f), — of -, 26(e). -out of turn, 22, 26(a), 26(g). Penalties for improper, 26. - when partner's turn, 26(g). -when under compulsion to pass, 26(b). Refuse defined, 39. Renounce. Opponent calls attention to -, 4I (b), 4I (c), LAWS OF CONTRACT BRIDGE 261 - becomes a revoke, 40. -- corrected, 41, 42. -defined, 39. -penalty, 4 (c), 42. Replacing packs, 2(d). Re'turning to table, 7, 8(b). Revoke. -avoided, 41. -defined, 40. -helps to win or defeat contract, 43(b). -in irregular trick, 34 (h), 34(j). Dummy not liable for, 41 (a). - on account of card short, 40 (d). -penalty, 43. "Protection from -," 41 (b). Renounce becomes -, 40. Time limit of -, 44. -when player fails to play as directed, 40(c). Rights. -at table, 6, 7, 8, 9. -of dummy, 30, 34(a). Room, first in, 6(a). Rubber. Cutting out at end of -, 9(b). Net points of -, 49(a), 52(c). Not starting - after specified time, 49(b). Premium for -, 52(b). Scoring unfinished -, 49 (b), 49(c). Unfinished -, 49(b), 49(c). When - begins and ends, 49 (a), Same dealer, 5, 6 (b). Same pack, 15. Score. -cancelled, 49(b), 49(c). Contract -, 36(a), 52 (a). 262 CORRECT CONTRACT BRIDGE Doubling -, 52(b). - for extra tricks, 52 (b). Game -, 47,52 (b). Honor —, 36 (a), 50 (b), 52 (b). Penalty -, 5 2 (b). Premium -, 52(b). Redoubling -, 52 (b). Slam -, 52(b). -stands, Is II. Undertrick -, 52 (b). Unfinished rubber -, 49(b), 49(c). Searching quitted tricks, 35(e), 40(b). Seats, choice of, 9(a), 9(c). Segregating tricks, 34(j), 35 (d), 40(b). Selection of penalty, 53. Senior. - defined, 29. -makes first lead, 30(a). Shuffle. -after the cut, I 2(b). Dealer may - last, Io(a). -described, Io. New -, io(d), I2(b). Side, I. Slam(s). -defined, 5. - earned by revoke, 43(b). -not affected by double or redouble, 25. Unbid -, 52(b). Value of -, 41, 52(b). Small slam, 5 (a), 52(b). Soiled cards, 2(c). Spades count thirty, 52 (a). Still pack. Missing cards found in -, 15 II. LAWS OF CONTRACT BRIDGE 263 Shuffled, Io(b). Substitutes, 8(a), 49(c). Substituting cards, 2(d), 42. Subtraction, error in, 52(f). Suits, rank of, 4, 35 (c) Table(s). Breaking up a -, 8 (b). Complete -, 6 (a). Cutting out of -, 9(b). Forming -, 6. Leaving -, 7, 8. Six members make complete -, 6 (a). Vacancies at -, 6, 7, 8. Ten exposed, 28. Termination of rubber at specified time, 49(b), 49 (c) Thirteenth card shown, 32(f). Too many or too few cards, I5 I, 34(h), 34(j), 40 (d). Torn cards, 2(C). Total score, 2 5(c). Touching a card, 14, 30(b-2), 3_ (c). Trick(s). Claiming and conceding -, 45, 46. Compulsory winning or losing of -, see Compulsory plays. -defined, 35 (b). Extra -, 37. -gained by revoke, 43 (b). gathered by wrong side, 35 (d). Giving information regarding winner of -, 54(b). Leading to -, 30(a), 35(a), 35(f). -gathered by wrong side, 35 (d). Looking at quitted -, 35 (e). 264 CORRECT CONTRACT BRIDGE Mixing -, 35 (d), 40(b). Number of - in book, 36(a), 38(a). Omitting playing to -, 34(h). Order of playing to-, 35 (a). Over six. - defined, 36(a). - value, 52(a). -when counted, 36. -where scored, 52(a). Playing to - makes revoke, 40(a-i). Quitted - containing fewer than four cards, 34(h). Quitted - containing more than four cards, 34(j). Segregating-, 34(j), 35 (d), 40(b). Trumping a -, 35 (c), 48. -values, 52(a). under -s, 38. Winning a -, 35 (c). Trump suit, 29, 35(c). Two or more cards exposed, 28, 32(a), 32(g), 34(b). Unauthorized information, 54. Unbid slams, 52(b). Undertricks, 38, 32(b). Unfinished rubber, 49(b), 49 (c) Vacancies at tables, 6, 7, 8. Values. Bidding -, 19. Honor -, 5o(b). -in general, 52. - of suits, 4. Trick-, 52(a). Vulnerable, 48, 52(b). Withdrawing from tables, 7, 8. LAWS OF CONTRACT BRIDGE 265 Wrong. -cut, I2(b), I6(a). -cutter, I2(b), I6(a). - deal, 15, i6. - dealer, 6 (a). -pack, i6(a). — penalty, 53 --score, 52(d), 52(e), 52(f). -side gathers trick, 35 (d). UNIVERSITY OF MICHIGAN 1 11 11ilI 1 1I 11 1 3 9015 01339 3759 ; ( 5 A)