JGV 1281 .R65 Copy 1 THE and OTHER AXIOMS of Bridge Whist EDMUND ROBERTSON. Price per single copy — 10 cents Fifty copies —4 dollars. NEW YORK Pl'DBfi of "Bollettino dellft *ei;t'. ITS Park Bow, 1903, THE ROBERTSON RULE and OTHER AXIOMS of Bridge Whist by EDMUND ROBERTSON. Price per single copy — 10 cents Fifty copies — 4 dollars. NEW YORK Fress of "Bollettino della Sera", 178 Park Row. 100%. THE LIBRARY OF CONGRESS, Two Comta Receives OCT, if 1902 CoPVBIOMT ENTRY CLASS ft-XXo, Wo, uzG(o c f Copyright 1902, By Edmund Robertson. THE ROBERTSON RULE. It is now pretty generally recognised that, in or- der to take full advantage of the deal/the chances that the expensive declarations present for making game should be first examined. Seeing that the value of each trick is highest in no trumps and that it is the shortest road to game, the dealer's first thought on looking at his hand should be: "Am I strong enough to go no trumps?" Before considering the measure of strength on which it would be sound to call no trumps it is ne- cessary to remember that the dealer has two impor- tant advantages. The first is the right to select the trump suit and the second is a knowledge of the cards he can depend upon to take tricks when Dummy's hand is placed on the table. The enormous advantage of knowing what cards are in his favor, where .finesses are praticable, and what suits have a chance of being established is alone sufficient to ensure the odd trick in no trumps with all round average hands — because the dealer not only sees but commands two hands. But this is not by itself a sufficient reason for calling no trumps with only an average hand. The odd trick in your deal is of. more value to the adver- saries than to yourself, because if they manage to score in your deal they will probably make game when it is their turn to declare trumps. If there is any doubt about the odd trick always make it a principle to pre- vent the adversaries from reaching one o-f the "useful" stages when they have the deal to go on with. It is therefore not sound to declare no trumps unless your hand contains at least one probable trick above the average, i, e., unless you are more or less certain of the odd trick and hope to score two by cards. There is another point to be considered. The lead being with the adversaries, if you are not protected in the majority of the suits, i. e., three (out of the four) it may happen that each of your opponents has a long suit and you may not get the lead in time to save the game. The general principle therefore on which it would be sound ti declare no trumps is that your hand should contain one very probable trick above the ave- rage with three suits protected. A suit is not absolutely protected in "no trumps", unless it contains one of the following combinations : Ace King King King Qn. Qn. Jack 7 io Qn. IO Jack IO 6 3 6 3 3 5 3 2 X Theoretically an average hand contains 3%. tricks Your hand taken with your partner's will on the ave- rage take 6y 2 tricks. If your hand contains one very probable trick above the average your combined hands will take at least seven tricks, i. e., you have a right to expect the odd trick, and may score two by cards. It becomes therefore very important to know what is an. average hand. There are four aces, kings, queens, &c, and the hand that contains an ace, a king, a queen,, a jack and a ten, i. e., a card of each denomination,, may be regarded as a typical average hand. But this arrangement is not usual. A hand may contain no ace or king and yet be of average strength. Without a measure of value it is very difficult, in the case of a mixed hand, to know whether it is above or below average strength. The following scale of values, known ar the "Robertson Rule", may be laid down for the purpose of calculating very nearly the exact strength of any hand : — ACE . . . . equal equal KING OUEEN JACK TEN equal equal equal to to to to to Total of an an average hand equal to 18 ;--,-■> r -i8 may therefore be regarded as the standard- of value of, an average hand. The value (5) assigned, to) the : King as compared, with the other Bridge honors- is a fraction too much, and those of the Queen, Jack, and Ten, too little, but these differences are quite in- appreciable in actual play, and may be safely disre- garded. It should be remembered that this scale of values is mainly intended tor the purpose* of- calculat- ing: the strength of a hand with a view to declaring no trumps and is based on the mathematical laws of chance. For the benefit of vacillators we will discuss this* valuation at some length. The beginner need not puzzle over the next six paragraphs. Every card has a threefold value : — (1) Its aggressive or trick-taking value. (2) Its obstructive value i. e., its power to prevent one or more adverse tricks. (3) Its protective value, i. e., its power to help other friendly cards to take tricks. What is the aggressive or trick-taking value of say, a guarded king in your hand without the ace of the same suit? There are three hands in one of which the ace must be, i. e., your partner has one chance out of three of holding the ace. Again, if your king is guard- ed (say you have K:ing,io,3) it should make a trick if the ace is held by the adversary ' to your right, i. e., there are two chances out of three that your king will make a trick. Assuming the trick-taking value of the ace at 1, the abstract trick-taking" value of the king is, therefore, in average positions, assuming that it is guarded, two out of three. The trick-taking value of the queen, jack and ten may be deduced in like manner. In average positions, assuming that it is guarded, the queen has four chances out of nine, the jack eight out of 27, and the ten 16 out of 8.1 of taking a trick. Reckoning the value (32-243) of the second Dutch honor, the nine, would seriously complicate matters, but it is a card by no means to be despised in no trumps. The value of a card, in so far as its power to prevent an adverse trick and its power to help friendly forces are concerned, is modified by so many circum- stances of position and play that it would be idle to lay down an exact scale of values. But in average positions the obstructive and protective values of the cards in a gradually descending scale from the ace downwards are relatively: — Ace ... ... ... . . . 81 King Queen jack Ten 54 36 24 16 Similarly the trick-taking worth of a card largely depends on what is termed the fall of the cards. In average position, however, the abstract threefold rela- tive values of the cards are very approximately : — Ace King Queen Jack Ten equal to 81 equal to 54 equal to 36 equal to 24 , eqal to 16 A possible objection to this scale of values is that only Bridge honors are taken into account, whereas small cards also score tricks. When a small card scores a trick (especially in no trumps) it can be proved to be due to the protective or obstructive value of one or more of the Bridge honors. Remember that this scale is mainly intended for the purpose of estimating the strength of a hand with a view to calling no trumps. There is no question in "no trumps" of a two of trumps ruffing an adverse ace. What you want to know is "How much above the average is my hand?" This scale will make the answer easy. Let us repeat the Robertson Rule for estimating an average hand : — ACE KING QUEEN JACK TEN > equal to 7 equal to 5 equal to 3 equal to 2 equal to 1 Average hand' equal to 18 Having - determined that the standard value of an average hand' is 18, the conclusion we arrive at is that with one ace (18 plus 7 equals 25) king (18 plus 5 equals 23) or queen (18 plus 3 equals 21) above average strength, i. e., with 21 points or over, and with three suits protected, it would be sound to declare no trumps. Remember that 21 points is the minimum strength on which it would be sound with the score at love all (the. score must always be considered) to declare no trumps, and three suits must be protected. This scale of values should not be applied to a Singleton Ace or King or an unguarded Queen, Jack or Ten. But every honor in a guarded suit must t>e given its full value. A Singleton ace, although a certain protection in one suit and a consideration as regards the honor value of the hand,loses virtue enormously in no trumps and should be reckoned at 4 only. Similarly Singleton King should be reckoned at 2 only (if your partner has not the ace it will force an adverse ace) and an unguarded queen at 1. SINGLETON ACE ... :.. equal to 4 SINGLETON KING . . . equal to 2 UNGUARDED QUEEN . . . equal to 1 An unguarded JACK or TEN need not be taken into account. The advantages of a measure of value for deter- mining a no trumps hand are enormous. Let us apply the test to the following, accepted no trumps hands. 8 Hearts - , ' i ' * Diamonds Clubs Spade-s A95- 7 Q.J 8.3 5 ; ^ ! 6. ' ; l a.k:7.2 12 25 K.Q.7.2 8 A.8.7. ; .7. 9.8. . A Q 6.5 10 25 K.Q.9.1. 8 Aid 8. 8 A.J.65.4.9 10 • ; 25 Hearts A.K6.2. 12 8.5. IC9 8 75. 5 Diatnands 6 , E.QJ.S 10 A.K4. 12 Clubs A.Q8.4, 10 , A.10.3. 8 Q. | Spades 3f.ro 9 T- 3 A. 9.7.2. 7 A.6.5.4. 7 25 2a 25 It will be noticed that these hands come, up to 25, i. e., seven points (an ace) above average strength, 18. They may be regarded as specimens of fine "no trum- pers." With two aces :;: there is always a probability" — ■ two chances out of three — of scoring 30 above the line, * To tail of into refinements: — Ace with one other ... King .".". Queen Jack ... ... In practice it is only necessary to remember that every honor in a guarded suit of not less that .three cams should be given its full value. equal to 6 equal to 4 equal to 2 equal to 1 9 which is about one-third of the rubber bonus ioo. Hands containing two aces, hot singletons or dou- l>letons,"and' a third suits absolutely guarded usually make the soundest no trumpers if they total up to 21 •tr over and there is no decided strength in a red suit. As we shall! see later, a hand well above average strength is not necessarily a u no trumper". There may foe^both more profit and more safety in a red trump ^declaration. With four aces (7 multiplied by 4 equals 28) there can be no doubt about the declaration. With three* aces (7 multiplied by .3 equals 21) unless there is sufficient strength in red suit to score game or a very large honor score the hand should as a rule be played without trumps. Besides the honor score (30) and three certain tricks, the protective and obstructive value of the aces are so great that the hand may be regarded as one very probable trick above average strength. : The value 7 assigned to the ace does not represent its trick-taking value alone, but its combined three- fold value. It may at first sight appear that as an ace, king, queen held in the same hand are equally valuable in no trumps they should be reckoned at 7 each. As however the protective value of the aces converts the king into certain trick and the combined protective values of the ace and and king help the queen to take a trick, their true values are 7, 5 and 3 respectively. *The honor value of: — 2 Aces ... ... ... equal to 2 3 " ... ... ... equal to 1 10 Other hands generally considered good enough for no trumps with the score love all: Hearts ' A.10.8.2. 8 A.Q.2. 10 7 6. Diamonds Q:X6. 5 J.10.7.3. 3 J.10 8 2! 3 Clubs K.Q3.2. 8 Q.8 5/ 3 Q J. 19- 3. 6 Spades 10 5. K.6.4. 5 A.K5. 12 21 ■ . , 21 ■v- 21 Hearts A.Q8.7. 9 A.7.6 ' 7 K10.3.2. 7 Diamonds K.10.9. 6 K J 0.8.2. 6 7.4 , ' . .i. Clubs QJ.10. 6 K.Q.9.3. 8 A.10.8. ■8 Spades 543 5.4. KJ9.6- 7 21 21 ■ 21 Remove even the lowest honor, the ten, from any- one of these hands and it will no longer be good enough for no trumps, as it will fall below the standard no trumper 21. These hands contain only a single ace each and are the minimum strength on which you should risk no trumps. Without an ace it is very seldom sound to go no- trumps. Besides a remote possibility of four aces being in one hand against the dealer, there is a pro- bability of losing 30 for honors. At love all or with the score in your favor no trumps should not be de- clared unless the hand totals up to. 25. But when only the odd trick is needed to score game or when the adversaries' score is so far advanced that onlv a bold II no trumper will save the game or rubber, the risk of an adverse honor score may be accepted, with a hand that totals up to at least 21. Hearts K. J. 9. 8. .. . , . : *■!.. %' Diamonds Q. J. 7 " . ... — 5', Clubs K. Q. 8 ... ~ ■-..'■;■ ... . 8; Spades K..J. 9 .... - .... 7/ "• -.'■•■ :,-,.. "■ . .. . .'•,;.'. .■•.-...' >i*f'4%: ' This fine hand is 'fully -asking -.and. a queen:, above average ^strength and' comes: up to 27. It is a soundl no trumper at almost any point of the score. The other three hands must hold j f6ur aces, a king, two queens* a .jack and four. tens, or a total of 45 points. The pro- babilities r are that' Dummy 'will hold his fair share of the good cards not in* your .hand', i. e., 45 1 3 equals 15^ This 15 and your 27 come up to 42. Playing on the probabilities these two hands are as much' superior in? trick-taking power tot. the adversaries' as' 42 is to 30 .(4 13). A superiority' of 7 to 6 is ail that is necessary to score the odd trick and owing to the dealer's advari-^ tages two by cards is more than probable- — with a fair prospect of game. As already pointed out, besides a. possibility of four aces being in one hand against you? there is a likelihood of losing 30 for honors, but there is at least an equal change of scoring 24 for tricks if not the game. In all doubtful cases the state of the score must decide the declaration. It should be noted that 21 is the minimum strength on which no trumps should be called with the score love all- — this minimum being increased or decreased according to the state of the score. When the score is decidedly in your favor, i. e., you are 24 or over,. unless you hold a fairly unbeatable no trumper (24 or over) you shoula search your hand to see whether yon have not a reasonable prospect of scoring game on a safer and less expensive declaration. But with the score dangerously against you an average hand or two five cards suits with two aces, or a six card suit headed by Ace, King, Queen, are good enough to risk: no trumps on. 12 II. A SYNOPSIS OF BRIDGE ■ . •• i j - ..- "..:■':-, DECLARATIONS . ;! o , ,., .— )o(— An attempt is made in this synopsis to cover the 'whole - field 5 of the declarations, by laying down: — (i) A standard minimum of strength on which certain ■■offensive declarations should be made origi- nally and on a pass. , (2) Arrstandard minimum, of weakness on which ^defensive declaration should be made originally. When once the beginner knows exactly what to declare at love all, be will soon be able to make his declaration fit the varying conditions of the score. The formulas given for no trumps, hearts and dia- monds are based on the mathematical laws of chance. They may at first sight appear to be too confusing to be applied in practice at the card table. Most hands. •however, do not admit of an alternative declaration, so that in practice it is only necessary to be acquainted with the Robertson Rule. In a percentage of hands, however, there usually exists a choice between two suits, or it may be a choice between two or more suits and a pass. In such cases it is clearly important to indicate the correct declaration. 'Generally speaking., when there is a choice be- tween no trumps and hearts thes latter should be selected, because it is an equally attacking declaration and as a rule very much the safer of the two. By equally attacking declaration is meant one that offers the same chance of game as a no trumper. At any point 01 the score only one trick more is needed with hearts as trumps to score game. This extra trick, if at cannot "be made by utilising one of Dummy's little trumps, may as a rule be secured by bringing in a long •card owing to the superior powers of re-entry that a long trump suit affords. When, there is a choice between no trumps and diamonds the Jailer, although it may be the safer of 13 the two declarations* falls ' away entirely from the attacking spirit of the deal, and should not, except when the dealer is. playing to the cScoreior /to the state of the rubber, be selected in preference to no trumps. The objects kept in view in makings out these formu- las are. — I. To enable a player to know what to declare at love , all, by ; laying down a standard^ minimum of strength on which certain declarations should be made originally and on a pass. , , * >• ->; -:■■■:%*. -r~ -To show the advantages of a hearts declara- tion when there is a choice between hearts-andyno trumps. V- ■;.- -;. :•;-" 3. To point out the disadvantages of a. diamonds declaration when there is a choice -between diamonds and no trumps. ; i,, 4. To show the dealer exactly when to use the spade shield. . , ..,.,''.':■■ 5. To correct the tendency of modern Bridge to shoulder Dummy with the responsibility of the de- claration. .-...•* OFFENSIVE DECLARATIONS BY THE DEALER AT LOVE ALL 7 ' NO TRUMPS. The dealer should declare no trumps if he has three suits guarded and his hand comes up to 21 or more, gauged by the Robertson Rule : Ace equal to 7. King equal to 5. ; f\ Queen equal to 3. Tack equal to 2. Ten equal to 1. % Singleton ace equal to 4. Unguarded king equal to 2. < Unguarded queen equal to 1. '■ The minimum for a no trumps declaration is 21 with three suits guarded. At love all or with the score in the dealer's favor 14 he should not declare no trumps without an ace unless his hand totals up to at least 25. As there are a large number of hands not 'guarded' in three 'suits which are quite' good enough for "no trumps", the dealer should see whether his- hand comes under The Seven Rule, which is that the dealer should declare no trumps With four tricks, and three suits guarded.,, '.. Five tricks and two suits guarded. Six tricks and one suit guarded. ■■•»;■ The declaration will, in fact, be theoretically corn rect if the number of tricks in hand plus. the number of suits guarded come up to seven or more. • ■ ■ .• - A five trick hand, two suits guarded, should'be* regarded as a strong attacking hand, and unless he has decided strength in a red suit, wich would certainly be the safer declaration, the dealer should unhesitat- ingly play without trumps. With six or more spades to the quint or quart major, even with three suits ab- solutely unprotected, the dealer at love all or with' the score against him should also declare "no trumps". A long solid suit of six or more cards gives the dealer a preponderating advantage in playing without trumps, and offers a chance of game that should not lightly be missed. It is a great mistake to suppose that every strong hand should be played without trumps. If the dealer's hand comes to 21 or more by the Robertson Rule and he also holds good hearts, there may be both more profit and more safetv in declaring hearts. A sound hearts declaration is the best of all possibile makes. HEARTS. The dealer should declare hearts if his hand totals up to 18 or more calculated dv this formula : Ace of hearts equal to 7. King of hearts equal to 5. Queen, Jack and 10 equal to 3 each. Every other heart equal to 2. 15 Every other* trick equal to 4. Every other probable trick equal to 2. For 3 honors add 4. For 4 honors add 16. This formula will enable the dealer to calculate the exact value of any hand with hearts as trumps. Should he, however, obtain a bigger result by calcu- lating the hand according to the Robertson Rule, he should of course declare no trumps and, vice versa. .. The formula may at first sight appear to be too confusing to be applied in actual practice at the card table This is not really so, because the ace, king and queen of hearts have the same values assigned to them as. in the Robertson Rule. All that the player need remember is that every heart, other than an honor, counts 2; every certain trick 4, and every probable trick 2. The value of three or more honors in hearts, is self-evident. Such hands hardly need the formula to be applied to them. So also with six or more hearts, hearts is with very rare exceptions the correct de- claration. The formula will, in fact, be only useful in cases of doubt between hearts and no trumps when the hand contains not more than five hearts. Such hands guarded in three suits are the only ones likely to admit of an alternative declaration. The minimum for a hearts declaration is 18. The dealer should not pass the declaration to Dummy if his hand comes up to this minimum. A detailed explanation of how this formula has been arrived at, together with a somewhat more ela- borate formula to ensure greater accuracy, will be * i. e., for every nearly certain trick, other than in the trump suit, such as an ace king or queen, add 4, and for every probable trick such as a guarded king or queen, jack, ten, other than in the trump suit, add 2. This formula is not intended to be applied to a hand containing only three hearts. When it is applied, to a hand containing only four hearts nothing should be added for three honors or less. She found in the Higher Grammar of Bridge,. It would be comparatively simple to lay down a formula for calculating the trick value of any hand and to show the different trick values of the same hand in the dif- ferent declarations. Unfortunately the honor-values of a "hearts", a "diamonds" and even a "clubs" hand and the aces in no trumps are disturbing elements which, completely destroy the simplicity of the calculation. The beginner need not puzzle over the explana- tion that follows. The face value of each trick in hearts as compared with "no trumps" is as 8 is to 12. But as four tricks, are wanted to score game from love all in hearts against three tricks in no. trumps the relative values are seemingly as 3 is to 4. But these values are further disturbed by the fact that in average positions with five or more cards of a suit the hand will score one trick more in a trump suit declara- tion than if played without trumps. This is usually the case with five hearts and almost invariably the case with six. So far therefore as scoring game in the deal goes, a hearts declaration if sound offers the same chance of making game, besides being the safer de- claration of the two. Taking all these facts into consideration in reckon- ing the value of the ace of hearts in no trumps and with hearts as trumps, the relative values are ap- proximately as 7 is to 6]/ 2 . Moreover the ace of hearts is an absolutely certain trick with hearts as trumps. It is not so in the dealer's or Dummy's hand in no trumps. In actual play such a fraction as 1 1 14 (the dif ference between 7 and 6 l / 2 divided by 7) is a negligible quantity. For this reason and for the sake of uniformity the value of the ace of hearts has been set down at 7. The honor value of the ace of hearts in either declaration is about the same. The trick taking relative value of the king of hearts, if deduced in like manner, will be approximate- ly 4. But the king of hearts, with hearts as trumps, has an honor value which it does not possess in play- ing without trumps. The honor values of the ace, king, queen, jack and ten are fully one each. The full value of the king therefore is approximately five. it Tfye queen, jack and ten possess an honor value of one each, plus their trick taking values which are de- pendent on their forming part of the trump suit. It would be sufficient, therefore for the purpose to ascertain the average trick value of any heart with hearts as trumps as compared with the value 7 (see the Robertson Rule) of a trick in no trumps. Takings 7 as the standard value of a trick in no trumps any fractional value less than half is quite inappreciable in actual play in any declaration. It is clear that the value of each heart will depend on the length of the suit. With five trumps in average positions after three rounds, the dealer will be left with two long trumps,, with six he will be left with three. Each heart may therefore be reckoned as a probable trick. According to the length of the suit their value would range between 2 and 3. With five only the value of each heart would be approximately 2, with six or more the value of each heart would be approximately 3. It is clear that in ruffing, in affording protection to other friendly cards, in helping to establish the dealer's or Dummy's suits, the longer the trump suit the greater the value of each individual trump. Ace of hearts equal to 7. King of hearts equal to 5. Queen, jack, and ten equal to 3 ecah. Every other heart equal to 2 or 3 according to the number of trumps in hand. In reckoning the value of each nearly certain and each probable trick outside the trump suit,it is tolera- bly clear that they lose value by being made in hearts at 8 points each instead of of in no trumps at 12 points each. This is especially so with aces. In reckoning the value of, say the ace of clubs with hearts as trumps i}/\ multiplied by 7 equals 21-4) it should be borne in mind that it has a distinct honor value in no trumps which it does not possess with hearts as trumps. At a liberal estimate, therefore, the value of each ace out- side the trump suit in a hearts declaration (% multi- plied by 7 minus 1) amounts to 4. Similarly the value of each probable trick outside the trump suit is 2. 18 Every nearly certain trick outside the trump suit is equal to 4. . • ■ Every probable trick outside the trump suit is •equal to 2. Owing- to the different honor scores for simple honors, double honors, and for four or more held in the same hand, it is obvious that a hand containing iliree honors (which mean 5 16 certain above the line and a probable 32) and a hand containing four ho- nors (64 above the line or about two-thirds the rubber ^bonus 100) have an increased value, which needs to Ibe separately taken into account. For 3 honors add 4, for 4 honors add 16.. DIAMONDS. Except with overwhelming strength, many for- ward players exclude diamonds aitogether from the list of original offensive declarations with the score love all, as this call offers a poor chance of game on the deal. This conservatism would be sound if the •average number of deals in a rubber were 3 or 4 or even 5. But experience has shewn that the average number of deals in a rubber is seven and a fraction, and that Dummy's chances of making a defensive de- claration on a pass are about 50 per cent. If imable to declare no trumps or hearts the dealer should see whether his hand comes up to the minimum IS for a diamonds declaration according to the follow- ing formula * : — Ace of diamonds 4. King of diamonds 3. Every other diamond 2. Every nearly certain trick outside the trump suit 3. Every probable trick outside the trump suit 1. Fot 3 honors add 3, for 4 honors add 12. A weak diamonds declarations, except to the score, is a very bad make. If the hand gives a bigger result when calculated by the Robertson Rule the dealer should unhestitat- *This formula is not intended for a hand that contains only four diamonds not all honors. 19 ingly declare no trumps. He should not pass the de- claration if his hand comes up to the minimum 15. CLUBS. An offensive clubs declaration should as a rule only be made to the score. With clubs however to four honors other than-A.K. Q.J. ten or A. K.Q. ten the dealer should declare clubs when he cannot see his way to making a more paying declaration, or is blank in the order suits. With ace, queen, jack, 10: or ace, king, jack, ten, or king, queen jack, ten and nothing else in the other suits, the dealer should declare clubs rather than pass the declaration, because the honor score, plus the probable trick score, will be found to be fully equal to the average value of a deal. In all other cases he should leave it to Dummy. • SPADES An offensive spades declaration except to the score is an absurdity. Defensive declarations by the dealer. THE SPADE SHIELD. When the dealers hand totals up to six or less by the Robertson Rule he should declare spades. This is an irreducible minimum, and should be regarded as the standard minimum of weakkness for an original defen- sive declaration. Without a winning c?rd in his hand the dealer should invariably declare spades unless he holds five clubs to two honors, or any six cards suit headed by an honor. With a six cards suit and nothing else in th^ hand it is clear that the hand is utterlv valueless unles^ the six cards suit be declared trumps. As a measur of protection, therefore, the dealer may be compelle to call hearts, with a hand like this : Heart: Jack, 9, 8, 7, 5, 4. Diamonds: 8, 4, 2. Club , Jack 9, 3. Spade : 8. 20 A DEFENSIVE CLUBS DECLARATION BY THE DEALER. The one exception to the above rule is when the dealer holds king, queen, jack and ten of clubs and not another remotely probable trick or any six cards suit. Clubs should then be declared defensively as well as for the sake of the honor score thirtytwo. PASSING THE DECLARATION. There is too great a tendency in modern Bridge to shoulder Dummy with the responsibility of the decla- ration With a four trick hand the dealer should make the most paying declaration he can — no trumps if pos- sible. As a rule, however, at love all with less strength than the minimum 21 for no trumps (see also the Seven Rule), 18 for nearts, 15 for diamonds, or d honors, in clubs, as seen above, he should pass the declaration to Dummy, but only if he holds one trick or a hand that totals up to at least 7 according to the Robertson Rule. As we have already seen, with less than this strength the dealer should make a protective declara- tion. At love all 7 should be regarded as an irreducible minimum for passing the declaration. OFFENSIVE DECLARATION BY DUMMY. At love all Dummy should declare : — No trumps if his hand comes to 22 by the Robert- son Rule. Hearts 18 (see the hearts formula) ; Diamonds 15 (see the diamonds formula). When an alternative declaration is open to Dummy he should calculate the hand by the Robertson Rule and the two formulas stated above, and make the de- claration that gives the biggest result. The Seven Rule should be worked with extreme caution on a pass. If Dummy holds a five trick hand, two suits guarded, he should not declare no trumps unless one of the 21 guarded suits is red. If both the guarded suits are red and neither of them sufficiently long to be mad- trumps Dummy should play without trumps. With only one long established suit, however, the long suit should usually be made trump. SPADES With less than the minimum strength, 22 for no trumps, 18 for hearts and 15 for diamonds, Dummy should have little hesitation in declaring spades, unless he holds at least six cards in another suit. Clubs should not be selected in preference to spades unless Dummy holds: 4 to 3 honors (when weak in spades), 5 to 2 honors, or 6 to 1 honor. The attempt to score off a poor hand marks the poor player. LIBRARY OF CONGRESS 020 237 428 1 . a pass. .^'guarded, one of ill e