The No-trump may be only of minimum strength, but it may, on the other hand, be of much more than average calibre. The Third Hand has yet to be heard from, and if, as is possible, he have considerable strength in the suit that the Second Hand thinks of declaring, such a bid will offer an ideal opportunity for a profitable double. The Second Hand, therefore, should be somewhat diffident about bidding two in a suit. He should make the declaration only when his hand is so strong that in spite of the No-trump, there seems to be a good chance of scoring game, or he has reason to think he can force and defeat an adverse two No-trumps, or the No-trump bidder is a player who considers it the part of weakness to allow his declaration to be easily taken away, and can, therefore, be forced to dangerous heights.

This is an opportunity for the Second Hand to use all his judgment. The Dealer may be taking desperate chances with a weak No-trumper, and the balance of strength may be with his partner and himself, in which case it is important for him now to show his colors; yet he must always keep in mind that conservatism, in the long run, is the main factor of Auction success. It is the ability (possibly "instinct" is the proper term) to act wisely in such cases that makes a bidder seem inspired.

With a strong Club or Diamond holding and a reentry, such a hand as, for example,—

Spades Two small Hearts Two small Diamonds King, Queen, Knave, and two small Clubs Ace, Knave, Ten, Nine

it is generally unwise to bid Second Hand over one No-trump.

There is little danger of the adversaries going game in No-trumps, but they may easily do so in Hearts or Royals. A Second Hand declaration in this position may point out to the opponents their safest route to game, and is not apt to prove of material benefit, as with such hand, eleven tricks against a No-trump is extremely improbable.

A similar principle presents itself when the holding is five of any suit, headed by the four top honors, or even by the three top honors, and no other strength. With such cards, the No-trump can almost certainly be kept from going game, and if the partner be able to assist, the declaration may be defeated. If, however, two of that suit be called, the adversaries, not having it stopped, will not advance the No-trump, but if sufficiently strong, will declare some other suit in which they may score game.

THE SHIFT

Holding six or more of a suit, headed by Ace, King, Queen, some writers have very properly called it an Auction "crime" to double. The question arises, however, "What should the Second Hand do under such circumstances?" A bid of two in his solid suit will eliminate any chance of the No-trump being continued, and an adverse call of two No-trumps is just what the holder of the solid suit most desires, as he can double with comparative safety, being assured both of the success of the double and of the improbability that the Declarer will be able to take himself out.

There has been suggested to meet this emergency a declaration called the "Shift." It consists in bidding two of a suit in which the Declarer has little or no strength. For this purpose a suit of lower value than the solid suit, should, if possible, be selected. The theory of the bid is that either the original No-trump declarer or his partner, having the suit securely stopped, will bid two No-trumps and that the double can then be effectively produced. The advocates of the Shift urge that should the worst happen, and the declaration be doubled, the player making it can then shift (this situation giving the declaration its name) to his real suit, and that no harm will ensue.

The trouble is that a double under such circumstances is not the worst that can happen. When the Shift was first suggested, players were not familiar with nor on the lookout for it. Success, or at least the absence of failure, therefore, often attended its use. Now, however, it is generally understood, and players will not either overbid or double a declarer they suspect of it. They merely allow him to meet his doom attempting, with weak Trumps, to win eight tricks against an adverse No-trumper.

While, therefore, at long intervals and under advantageous circumstances, the Shift may be successfully utilized, against experienced players it is a dangerous expedient, especially for any one known to be fond of that character of declaration.

The conservative and safe course to follow with a holding of the character described is to pass the one No-trump.

WHEN TO BID TWO NO-TRUMPS OVER ONE NO-TRUMP

The bid of two No-trumps over one No-trump is a more or less spectacular performance, that appeals to those fond of the theatrical. There are some hands that justify it, but it is safe to say that in actual play it is tried far more frequently than Second Hand holdings warrant.

Such a bid may be made with a strong suit—not of great length—and the three other suits safely stopped, with the four suits stopped twice, with a long solid Club or Diamond suit and two other suits stopped, or with some similar, and, under the circumstances, equally unusual combination.

HOW TO BID AGAINST TWO OR THREE SPADES

With two Spades bid by the Dealer, if the Second Hand have a suit he desires led against a No-trump, it is of the utmost importance that he indicate it to his partner.

Under such conditions, the Second Hand should declare a suit headed by King, Queen, Knave, or some similar combination, but should avoid bidding a long, weak suit, as the No-trump declarer may hold Ace, Queen of it, and the partner may, by the call, be invited to lead his King into the jaws of death. Of course, if the hand contain reentries, it may be advisable to make such a bid, although even then it may advantageously be delayed until the second round, since against a two Spade declaration the Second Hand is sure of having another opportunity to speak.

With three Spades declared by the Dealer, the Second Hand expects a Royal from the Third Hand. He knows that he will have another chance to bid, but, as he will then probably have to go much higher, it is just as well not to wait if the hand contain any advantageous declaration.

WHEN TO BID NO-TRUMP OVER A SUIT

The question of what amount of strength warrants the Second Hand in bidding one No-trump, after a suit has been declared by the Dealer, is somewhat difficult to accurately answer. It goes without saying that to justify a No-trump under such circumstances, the Second Hand must have much better than merely an average holding. The suit that the Dealer has bid should be safely stopped, and when the declarer has only one trick in that suit, at least four other tricks should be in sight.

Occasionally cases arise in which the Second Hand may bid one No-trump over a suit declaration without the suit that has been declared being stopped, but these are rare and such a call should only be made with unusual strength, as it gives the partner the right to assume that the adverse suit is stopped and he may consequently advance the No-trump to dangerous figures.

It is probably a good rule that a No-trump should not be called over a declared suit, that suit not being stopped, with a holding of less than six sure tricks. Even with one stopper in the suit bid, it is generally better to declare either Royals or Hearts in preference to No-trump, provided the hand contain sufficient length and strength to warrant such declaration.



IV

THIRD HAND DECLARATIONS

Third Hand declarations can best be considered by dividing them into three classes:—

1. When the Dealer has called one Spade, and the Second Hand passed.

2. When the Dealer has made an offensive declaration, and the Second Hand passed.

3. When the Second Hand has declared.

The distinction between these three situations is so clearly drawn that each is really a separate and distinct subject. They will be taken up seriatim.

WHEN THE DEALER HAS CALLED ONE SPADE, AND THE SECOND HAND PASSED

In the old days, when the Dealer's "one Spade" was without significance, the Third Hand was always obliged to declare, in order to give the Dealer the opportunity to get back into the game, as it was possible that he had great strength. Now the Third Hand recognizes that there is not the least obligation upon him to bid, and that it is inadvisable for him to do so unless his hand be so strong that, even with a weak partner, game is in sight, or unless it be important for him to indicate to the Dealer what to lead if the Fourth Hand make the final declaration.

Should the Third Hand pass, and the Fourth Hand also pass, allowing the one Spade declaration to stand, the liability of the Declarer cannot exceed 100 points, but if the Third Hand bid, the liability becomes unlimited. While the Dealer and Second Hand both have the right to assume that their partners have an average percentage of the remaining cards, the Third Hand is not justified in any such presumption, after the Dealer, by bidding one Spade, has virtually waved the red flag. True it is, a similar warning has appeared on the right, but if both danger signals are to be believed, the only inference is that the strength is massed on the left. The bidding by the Third Hand must, therefore, be of a very different character from that of the Dealer or Second Hand. He should not venture a No-trump unless he have four sure tricks with the probability of more and at least three suits stopped. When in doubt whether to declare No-trump or a suit, it is generally wise for him to select the latter.

Third Hand suit declarations should be made under either of two conditions:—

(a) When the hand is so strong that there appears to be at least a fair chance for game with the suit he names as Trump.

(b) When he expects a No-trump from the Fourth Hand and wishes to indicate to his partner the lead he desires.

In the former case, it is often good policy for the Third Hand to start with a bid of two. This serves a double purpose, as it shows the Dealer the character of the hand and helps to shut out an adverse declaration.

If the main idea of the bid be to indicate a lead, it is advisable to make it on the first round, when one can be called, rather than wait until it becomes necessary to bid two, which, against a No-trump, may prove dangerous. If the Third Hand have any such combination as King, Queen, Knave, with one or more others of that suit, and a reentry, a declaration at this stage is most important, as unless the partner open that suit, it will probably never be established against a No-trump. Even if the long suit be headed by Queen, Knave, it may be important to show it, as the partner may hold an honor, in which case the suit may be quickly established. When the long suit is headed by a Knave, it should not be shown unless the hand contain more than one reentry. It may be so necessary for the Third Hand, in the position under consideration, to indicate a lead that no absolute strength requirement, such as a fixed number of tricks, is essential for a bid. It frequently keeps the adverse No-trumper from going game to have the right suit called originally—otherwise, the Dealer has to lead his own suit, and when the Third Hand is without strength in it, such a lead greatly facilitates the Declarer.

WHEN THE DEALER HAS SHOWN STRENGTH AND THE SECOND HAND PASSED

One of the cardinal principles of harmonious team play is that when the partner has made a suit declaration which is apt to result in game, it is inadvisable to "take him out" merely with the hope of obtaining a slightly higher score. Suppose the partner has declared a Heart and the Third Hand holds three Hearts, headed by the Ace, four Clubs headed by the King, no Diamonds, and five Spades with three honors. Of course, the partner may have an honor and some other Spades, and, therefore, a bid of Royals may produce a higher count than Hearts, but that is only "may." The Declarer certainly has Heart strength, and the Third Hand, valuable assistance. It takes the same number of tricks to score game in each suit. Why, therefore, risk the game for a paltry addition to the trick and honor score?

One of the most remarkable features of Auction is the extraordinary desire, exhibited by a large percentage of players, to play the combined hands. This comment is not applicable to a strong player, who, for the good of the partnership, is anxious to get the declaration himself, in order that during the play two or three tricks may not be presented to the adversaries, but is intended for the general run of cases where the partners are of equal, or nearly equal, ability.

A player, before determining to overbid his partner's call, should remember that one of the greatest pleasures of the game is facing the Dummy, especially when the declaration is apt to be successful, and he should assure himself beyond peradventure that, in bidding his own suit in preference to advancing his partner's, he is not in any way influenced by his own selfish desires. He should be sure that, with the positions reversed, he would thoroughly approve of just such action by his partner; and, if his partner be the better player, he should also convince himself that his suit is at least two tricks stronger, as his partner's superior play probably makes a difference of at least one in favor of his declaration.

It should be put down as axiomatic that, when a partner takes out a Heart or Royal with a bid of another suit, he denies strength in the suit originally declared and announces great length with probably four honors in the suit he names; also, that when a Heart or Royal is taken out by a No-trump declaration (except with a four-Ace holding), not only is weakness in the declared suit announced, but also the fact that every other suit is safely stopped.

This must not be understood as a suggestion that a partner should seldom be overbid. Quite the reverse. The informatory school of modern bidding, which attempts, as nearly as possible, to declare the two hands as one, has as an essential feature the overbidding of the partner in an infinite number of cases. It is against the foolish and selfish instances which occur with great frequency that this protest is directed.

WHEN "TWO SPADES" HAS BEEN DECLARED

When the Dealer bids two Spades, he gives explicit information regarding the contents of his hand.[9] The Third Hand is, therefore, practically in the position of having twenty-six cards spread before him, and the question of what he should declare is not apt to be at all confusing.

[9] See page 47.

If his hand be trickless, or practically so, he must bid one Royal, as that reduces the commitment from two tricks to one, and increases the possible gain per trick from 2 points to 9.

It is a noncommittal bid, as it may be made with great weakness or moderate strength. With considerable Spade strength, however, two Royals should be declared.

When the Third Hand has other than Spade strength, he will, of course, bid in accordance with his holding, but it goes without saying that he should make the best possible use of the accurate information he has received. With four strong Spades, even with sufficient additional strength to justify a weak No-trump, a Royal is generally preferable, and with more than four Spades, two Royals is unquestionably the bid, regardless of the strength of the remainder of the hand, unless, of course, it contain the much looked for, but seldom found, four Aces.

WHEN "THREE SPADES" HAS BEEN DECLARED

When the Dealer has called three Spades, the Third Hand has quite accurate data with which to work.[10] In this case, even if his hand be trickless, he must bid one Royal, as his partner's three Spades might otherwise be left in by the Fourth Hand. With some strength in other suits, one Royal is his bid, unless his cards justify him in telling the Dealer that, in spite of the announced long, weak Spades, the combined hands are apt to sail more smoothly and on more peaceful seas to the port called "Game" by the No-trump than by the suggested Royal route.

[10] See page 49.

Should the Third Hand overbid three Spades with either Hearts, Diamonds, or Clubs, he shows great strength in the suit named and absolute weakness in Spades; the bid of two Royals shows assistance in Spades, and probably other strength.

WHEN "ONE CLUB" OR "ONE DIAMOND" HAS BEEN DECLARED

When the Dealer has called one Club or one Diamond, the Third Hand (the score being love) must realize that going game with the declaration made is most unlikely. He should, therefore, overbid it whenever he has sufficient strength to justify such action. With strong Hearts or Spades, he should bid Hearts or Royals; without such Heart or Spade strength, but with three tricks and two suits stopped, he should bid No-trump. In the rare case in which game seems probable with the Club or Diamond declaration, he should advance his partner's call to two or three.

WHEN "TWO DIAMONDS" OR "TWO CLUBS" HAS BEEN DECLARED

When the Dealer has called two Clubs or two Diamonds with the score at love, the Third Hand should allow the declaration to stand, unless his Heart or Spade holding be such that he believes, with the assistance of his partner's Club or Diamond suit, he may win the game; or unless able to bid two No-trumps. With the information that his partner has an established suit, it does not require much strength to justify the two No-trumps call. With all the other suits stopped, no matter how weakly, the bid is imperative. With two securely stopped, it is advisable, but with only one stopped, it is entirely out of the question.

With a score in the trick column, the Third Hand will treat either a one or two Club or Diamond declaration just as, with the score at love, he treats a similar call in Hearts or Royals.

WHEN "ONE HEART" OR "ONE ROYAL" HAS BEEN DECLARED

When the Dealer bids one Heart or one Royal, the Third Hand should not overbid unless without strength in the declaration. By this is meant not only the absence of high cards, but also the absence of length. With four small Hearts or Spades, and that suit bid by the Dealer, it is almost invariably the part of wisdom to allow it to remain.

The Third Hand should bid one Royal over one Heart, or two Hearts over one Royal with strength sufficient to justify an original call in that suit, and distinct weakness in the partner's declaration. The theory is that the Third Hand knows he cannot help his partner's declaration, while it is possible his partner may help him.

When the Third Hand has such strength in Hearts or Royals that he would advance his partner's declaration of either, in the event of an adverse bid, it is wise for him to bid two on the first round, in order, if possible, to shut out such adverse declaration and the information thereby given to the leader.

The Third Hand should call two Diamonds or Clubs over one Heart or Royal when he holds a long and practically solid suit. The original bidder can then use his judgment whether to let this declaration stand, continue his own, or try two No-trumps.

With a score, two Clubs or Diamonds may be bid more freely over the partner's Heart or Royal.

The Third Hand should not bid a No-trump over the Dealer's Heart or Royal, unless he have the three remaining suits safely stopped, or his hand contain solid Diamonds or Clubs, and one other suit stopped.

WHEN "TWO HEARTS" OR "TWO ROYALS" HAS BEEN DECLARED

The declaration of two Hearts or two Royals is practically a command to the partner not to alter the call. It indicates at least six sure tricks, probably more, and a valuable honor count, in the Declarer's hand, provided the suit named be the Trump. The Third Hand should only change such a declaration when convinced beyond reasonable doubt that his holding is so unusual that he is warranted in assuming the responsibility of countermanding the order that has issued.

Weakness in the Trump and strength in some other suit is far from being a sufficient justification, as the chances are that the Dealer is weak in the suit of the Third Hand, and called "two" mainly for the purpose of keeping it from being named. To overbid two Royals or Hearts with three Diamonds or Clubs is obviously absurd, unless holding five honors and such other strength that game is assured.

To overbid two Hearts with two Royals, or two Royals with three Hearts, is almost tantamount to saying, "Partner, I know you are trying to shut out this declaration, but I am strong enough to insist upon it." Such action is only justified by 64 or 72 honors, and a sure game.

To overbid two Hearts or two Royals with two No-trumps, as a rule, means 100 Aces. High-card strength assures the game in the partner's call with probably a big honor score; only the premium of 100 makes the change advisable.

With strength, in the case under consideration, the Third Hand should advance his partner's call with much greater confidence than if it were an ordinary bid of one. He should not worry even if absolutely void of Trumps; in that suit his partner has announced great length as well as commanding cards; Aces and Kings of the other suits are what the Declarer wishes to find in his hand, and with them he should bid fearlessly.

The same line of comment applies with even greater force to the action of the Third Hand when the Dealer has bid three Royals or three Hearts.

WHEN TO OVERBID A PARTNER'S NO-TRUMP

When the Dealer bids one No-trump and the Third Hand holds five or more of any suit, one of the most disputed questions of Auction presents itself.

The conservative player believes that with five Hearts or Spades, inasmuch as but one more trick is required to secure game, it is safer to bid two Hearts or Royals, except, of course, when the Third Hand, in addition to a five-card suit, has the three remaining suits stopped. The theory is that if the combined hands are very strong, the winning of the game is absolutely assured with the suit in question the Trump, but may possibly be lost in the No-trump by the adversaries running a long suit. The chance of a hostile suit being established is unquestionably worthy of the consideration of the Third Hand whenever, with great strength in Hearts or Spades, he allows his partner's No-trump to stand. Five adverse tricks prevent a game. In the majority of cases, the leader opens a five-card suit. When it is not stopped, the game is saved by the adversaries before the powerful No-trump hand can get in; if it be stopped but once, the game is still in grave danger unless the Declarer take nine tricks before losing the lead.

With a Heart or Royal declaration the adversaries are not apt to take more than two tricks in their long suit, which, at No-trumps, may produce four or five (in rare cases six), and yet the Trump bid requires only one more trick for game.

It is unquestionably true that, with great strength, the game will be won nine times out of ten with the No-trump declaration, but in every such case it is absolutely "cinched" by the Heart or Royal call.

It is further argued that, when the combined hands are not quite so strong, a game is more frequently won with the Trump declaration, as the small Trumps are sure to take tricks, but the long suit may not be established in the No-trumper.

The believers in taking a chance, however, view the situation from the opposite standpoint. Their argument is that the game requires one more trick, when a Trump is declared, but does not count as much, that the original declarer may be weak in the suit named, yet strong in all the others, and therefore, with a good hand, it is wiser to leave the No-trump alone.

It is possible that the question is one rather of the temperament of the player than of card judgment. It is susceptible of almost mathematical deduction that five or more cards of a long suit are of greater trick-taking value when that suit is the Trump than when No-trump is being played, and it does not require any argument to substantiate the proposition that the slight difference in the score, between the total in the trick and honor columns netted from a game made without a Trump and a game made with Royals or Hearts, is so infinitesimal as not to be worthy of consideration. Nevertheless, players possessed of a certain temperament will, for example, refuse to overbid a partner's No-trump with Ace, King, Ten, and two small Spades, King of Hearts, and Ace of Diamonds, on the ground that the hand is too strong, although the No-trump bid may have been thoroughly justified by such a holding as Ace, Queen, Knave, of Hearts; King, Queen, Knave, of Diamonds; and Queen, Knave, of Spades. In that event it is practically sure the adversaries will open the Club suit and save the game before the Declarer has a chance to win a trick. This and similar situations occur with sufficient frequency to make them well worthy of consideration, and when such a hand fails to make game, it certainly seems to be a perfect example of what might be termed "useless sacrifice."

In spite of all this, however, probably as long as the game lasts, in the large proportion of hands in which the taking-out does not make any difference, the Declarer will say, "With such strength you should have let my No-trump alone"; or the Dummy will learnedly explain, "I was too strong to take you out."

It would be in the interest of scientific play, if, except when all suits are stopped, the theory, "Too strong to take the partner out of the No-trump," had never been conceived, and would never again be advanced.

The same comment applies with equal force to the remark so often heard, "Partner, I was too weak to take you out."

This generally emanates from a Third Hand who has a five- or six-card suit in a trickless hand. He does not stop to realize that his hand will not aid his partner's No-trump to the extent of a single trick, but that in a Trump declaration, it will almost certainly take two tricks. The Trump bid only increases the commitment by one, so it is obviously a saving and advantageous play. Furthermore, it prevents the adversaries from running a long suit. It, also, in Clubs and Diamonds, is a real danger signal, and, in the probable event of a bid by the Fourth Hand, warns the partner away from two No-trumps.

The advocates of the weakness take-out realize that in exceptional instances the play may result most unfortunately. When the Dealer has called a border-line No-trump, without any strength in the suit named by the Third Hand, and one of the adversaries has great length and strength in that suit, a heavy loss is bound to ensue, which may be increased 100 by the advance of the bid from one to two. This case is, indeed, rare, and when it does turn up the chances are that the Declarer will escape a double, as the holder of the big Trumps will fear the Dealer may be able to come to the rescue if he point out the danger by doubling the suit call.

The fact, however, that a play at times works badly is not a sufficient argument against its use, if in the majority of cases it prove advantageous, and that is unquestionably true of the weakness take-out.

The strength take-out, above advocated, applies only to Spades and Hearts. With Diamonds and Clubs, at a love score, the distance to go for game is in most cases too great to make it advisable, but the weakness take-out should be used equally with any one of the four suits, as it is a defensive, not an offensive, declaration. With a score, Clubs and Diamonds possess the same value that Hearts and Spades have at love, and should be treated similarly.

WHEN TO OVERBID WITH STRONG CLUBS

The question of whether the Third Hand, with strong Clubs, should overbid his partner's No-trump has aroused considerable discussion. The argument in favor of such a declaration in Clubs, which does not apply to any other suit, is that the difference between a strength and a weakness overbid can be made apparent by calling three and two respectively, and yet the show of strength will not force the Dealer higher than two No-trumps, when his hand is such that the announcement that the Third Hand holds strong Clubs, but nothing else, makes the return to No-trump advisable.

On this basis of reasoning some believe in calling three Clubs whenever an otherwise trickless Third Hand contains five or more Clubs headed by Ace, King, Queen. This, it is conceded, only results advantageously when the No-trump has been called with one suit unguarded, and Clubs is one of the protected suits. When the No-trump has been declared with such a hand as

Spades Ace, King, X Hearts X Diamonds Ace, King, Knave, X, X Clubs Knave, Ten, X, X

the employment of such a system of declaration is exceptionally advantageous; as the game is assured in Clubs, while if the No-trump be left in, the adversaries will probably save it by making all their Hearts before the Declarer secures the lead.

It is admitted that this case is somewhat unusual, but the advocates of the system, conceding this, argue it is advantageous to have this bid in the repertory, and, in the exceptional instance, to obtain the benefit, which is bound to ensue from its use. The contention is that it can do no harm, with such a Club holding, to force the partner to two No-trumps, if he have all the other suits stopped, and the fact that three Clubs is called with strength more clearly accentuates the principle that the two Club takeout means nothing but weakness.

Admitting the force of this argument, and conceding that the system advocated should be universally adopted were there not a wiser use for the three Club take-out, first brings forth the question of whether the case does not more frequently arise in which the long Club holding of the Third Hand is headed by King and Queen, and is it not much more probable, when the Third Hand has long Clubs, that the No-trump maker has the suit stopped with the Ace than with four headed by Knave, Ten?

It must be remembered that the three Club take-out with Ace, King, Queen, at the head of five or more, is only advantageous when the No-trump has been called with a hand in which only three suits are stopped, of which the Club is one. If the Club be the suit unstopped, the call merely forces an advance in the No-trump.

If, however, the convention be to use three Clubs to overbid the partner's No-trump only when holding an otherwise trickless hand which contains either at least five Clubs headed by King, Queen, Knave, or at least six headed by King, Queen, would not the number of instances in which the call proves of benefit appreciably increase, and would not every reason applicable in the former case be even more forceful in the latter?

It cannot be questioned that the partner having called No-trump, the Third Hand is more likely to hold either five Clubs headed by King, Queen, Knave, or six headed by King, Queen, than five or more headed by Ace, King, Queen. The greater probability that the Dealer will have the Ace than four headed by Knave, Ten, is just as obvious.

Take such a No-trump declaration as

Spades Ace, King, Knave Hearts X, X Diamonds Ace, King, Knave, X, X Clubs Ace, X, X

and the advantage of the proposed system becomes apparent. The game, which is almost sure to be lost by the Heart lead in No-trump, becomes almost a certainty with Clubs Trump. When this plan is used and the Dealer has the other suits stopped but has not the Ace of Clubs, he can easily decide whether to go to two No-trumps, as he can estimate from the length of his Club holding whether he can establish the long Clubs or the adverse Ace will block the suit. When the latter is the case, he should not bid two No-trumps unless his own hand justify it, as the Third Hand has announced the absence of a reentry.

Take such a No-trump declaration as

Spades Ace Hearts Ace, King, X Diamonds Ace, King, X, X, X, X Clubs X, X, X

and suppose the Third Hand hold one or two small Diamonds; six Clubs, headed by King, Queen, Knave, and no other face card.

In such a case Clubs is the call most likely to produce game.

Another and possibly the wisest theory of the three Club take-out, is that it should be reserved, not for any one particular holding which may not occur once in a year, but for any hand in which the Declarer wishes to say, "Partner, my cards are such that I believe we can go game in Clubs; with this information, use your judgment as to whether or not to return to your more valuable declaration."

A NEW PLAN FOR OVERBIDDING

In this connection, a new scheme of take-out is respectfully called to the attention of the thoughtful and studious Auction players of the country. It is not in general use, is not recognized as conventional, has never been given a satisfactory trial, and is, therefore, suggested merely as an experiment worthy of consideration.

The idea is that when a partner has called one No-trump, Second Hand having passed, the Third Hand with five or more Spades or Hearts, unless he have four suits stopped, should bid his long suit in the following manner: if the hand be weak, the bid should be two; if strong, three. This warns the Dealer, when two is called, to let the declaration alone, as it is defensive.

On the other hand, when three is bid, the Dealer knows that his partner is strong, and he may then use his judgment as to the advisability of allowing the bid to stand or going back to the No-trump, which he can do without increasing the number of tricks of the commitment.

It must be remembered that, with great strength, it is as easy to make three No-trumps as one, three are needed for game, and, therefore, nothing is lost by the expedient.

Playing under this system, should the Third Hand hold four or five honors in his suit, and earnestly desire to play it for the honor score, it would be a perfectly legitimate strategy to deceive the partner temporarily by bidding two, instead of three.

WHEN TO OVERBID ONE NO-TRUMP WITH TWO NO-TRUMPS

When the Dealer has bid one No-trump and the Second Hand passed, the Third Hand, much more frequently than most players imagine, should call two No-trumps. It must be remembered that should the Third Hand pass, the Fourth Hand can, by bidding two of a suit, indicate to his partner the lead he desires. This places the adversaries in a much more advantageous position than if the leader open his own suit without information from his partner. The bid of two No-trumps by the Third Hand generally prevents the Fourth Hand from declaring, as it necessitates a call of three, which, sitting between two No-trump bidders, is, in most cases, too formidable a contract to undertake.

It is, therefore, advisable for the Third Hand, on the first round, to advance, from one to two, his partner's No-trump declaration, in every instance in which, in the event of an adverse bid, he is strong enough to call two No-trumps. This convention, while as yet comparatively new, and, therefore, but little used, works most advantageously, as it frequently shuts out the only lead which can keep the No-trump from going game. It is important for every player to understand the scheme, and never to overlook an opportunity to make the declaration.

WHAT THIRD HAND SHOULD BID WHEN SECOND HAND HAS DECLARED

This situation involves so many possibilities that it is hard to cover it with fixed rules.

The Third Hand in this position should reason in very much the same manner as the Second Hand, after the Dealer has made a declaration showing strength.[11] There is this distinct difference, however: in the case of the Second Hand, he only knows that the Dealer has sufficient strength to declare, and is without any means, other than the doctrine of chances, of estimating the strength of his partner's hand. The Third Hand, however, in the situation under consideration, is not only advised that one adversary has sufficient strength to declare, but also knows whether his partner's cards justify an initial bid. When the Dealer has shown strength, he can be counted upon for at least the minimum that his bid has evidenced; when he has called "one Spade," it would not be wise to expect him to win more than one trick.

[11] See page 72.

The Third Hand should consider these features of the situation, and satisfy himself, when his partner has not shown strength, that he is taking a wise risk in bidding over an adverse declaration. To justify a call of No-trump over a Trump, he should either have the declared suit stopped twice or, if it be stopped but once, he should also have solid Clubs or Diamonds. When the Dealer has declared Hearts or Royals, and the Second Hand made a higher suit call, it is, as a rule, wiser for the Third Hand to advance his partner's declaration than to venture a No-trump unless he have the adverse suit stopped twice.

When the Dealer has bid No-trump and the Second Hand two of any suit, the Third Hand should not bid two No-trump unless he have the declared suit stopped and at least one other trick. Without the declared suit stopped, he should not bid two No-trump unless his hand be so strong that he can figure with almost positive certainty that the No-trump bid of his partner could not have been made without the adverse suit being stopped. When in doubt, under such conditions, as to the advisability of either bidding two No-trumps or some suit, the latter policy is generally the safer.

When the Dealer has called No-trump and the Second Hand two of a suit, the Third Hand must realize that his partner has already been taken out, and therefore, under no circumstances, should he bid in this situation, except for the purpose of showing strength; or with the conviction that, aided by his partner's No-trump, he can fulfil the contract he is proposing. For example, Dealer bids one No-trump; Second Hand, two Royals; Third Hand holds six Hearts, headed by the Knave, without another trick. Under these conditions, a Heart bid would be most misleading, and probably most damaging. The Dealer may not be able to help the Heart declaration, and he may very properly be encouraged by it to believe that the Third Hand has considerable strength, especially in Hearts, but is very weak in Spades. If, in consequence of this supposed information, he return to his No-trump declaration, or double an adverse three Royals, the result is apt to be extremely disastrous.

The Third Hand must distinguish this case carefully from the situation in which the Dealer has bid one No-trump and the Second Hand passed. With the combination mentioned, he should then, of course, most unhesitatingly take out his partner by bidding two Hearts; that bid, under such circumstances, not showing strength.

Another situation that arises more frequently than would be supposed, and the advantage of which it is most important for the Third Hand to grasp, is when the Dealer has bid No-trump; the Second Hand, two of a suit; and the Third Hand, without the adverse suit stopped, holds great strength in Clubs, with such a hand that he desires his partner to go to two No-trumps; provided he have the adversaries' suit stopped. The bid of three Clubs does not increase the No-trump commitment which the partner is obliged to make, and is much safer than for the Third Hand to bid two No-trumps without the adverse suit stopped. It is a suggestion to the partner to bid two No-trumps, provided he can take care of the suit which the Second Hand has declared.



V

FOURTH HAND DECLARATIONS

Some of the principles that have been considered in connection with certain Second and Third Hand bids are also applicable to similar Fourth Hand declarations. These are easily pointed out, but the bidding by the Fourth Hand presents other problems much more difficult.

Each player who has an opportunity to declare materially complicates the situation, and makes it harder to accurately describe. As three players declare or pass before the Fourth Hand has his turn, it is almost impossible to anticipate every contingency that may arise. The best that can be done is to subdivide Fourth Hand declarations as follows:—

1. When the Dealer's defensive declaration has been the only bid.

2. When the only offensive declaration has been made by the Dealer.

3. When the only offensive declaration has been made by the Second Hand.

4. When the only offensive declaration has been made by the Third Hand.

5. When the Dealer has made a defensive, and both the Second and Third Hand, offensive declarations.

6. When the Dealer and Second Hand have made offensive declarations and the Third Hand passed.

7. When the Dealer and Third Hand have made offensive declarations, and the Second Hand passed.

8. When all three players have made offensive declarations.

1. WHEN THE DEALER'S DEFENSIVE DECLARATION HAS BEEN THE ONLY BID

As a general rule, when this situation arises, the Fourth Hand holds a combination of cards which makes his bid unmistakable. The other three players having shown weakness, or, at least, the absence of offensive strength, the Fourth Hand almost invariably has a No-trumper of such strength that his pathway is plain. Of course, his hand may, by reason of Spade or Heart length, call for a Royal or Heart declaration in preference to a No-trumper, but nevertheless, under these circumstances, it is generally easy for the Fourth Hand to declare.

When, however, the exceptional case occurs, in which the Fourth Hand finds himself, no previous offensive declaration having been made, without a plainly indicated bid, it is difficult to lay down a rule for his guidance. Three players have shown weakness, and yet his cards assure him that one or more of them is either unduly cautious, has passed by mistake, or is trying to deceive. If the strength be with his partner, it may be that, by passing, he will lose an opportunity to secure the game. On the other hand, if the adversaries have the winning cards, he may, by declaring, allow them to make a game declaration, whereas they are now limited to an infinitesimal score.

He must also consider that, should he pass, the maximum he and his partner can secure is 100 points in the honor column. This is a position to which conventional rules cannot apply. The individual characteristics of the players must be considered. The Fourth Hand must guess which of the three players is the most apt to have been cautious, careless, or "foxy," and he should either pass or declare, as he decides whether it is more likely that his partner or one of the two adversaries is responsible for his predicament.

It sometimes, although rarely, happens that the strength not in the Fourth Hand is so evenly divided that no one of the three has been justified in making an offensive declaration, and yet the Fourth Hand is not very strong. When this occurs, a clever player can as a rule readily and accurately diagnose it from the character of his hand, and he should then pass, as he cannot hope to make game on an evenly divided hand, while as it stands he has the adversaries limited to a score of 2 points for each odd trick, yet booked for a loss of 50 if they fail to make seven tricks; 100, if they do not make six. In other words, they are betting 25 to 1 on an even proposition. Such a position is much too advantageous to voluntarily surrender.

It is hardly conceivable that any one would advocate that a Fourth Hand player with a sure game in his grasp, instead of scoring it, should allow the adverse "one Spade" to stay in for the purpose of securing the 100 bonus.

Inasmuch, however, as this proposition has been advanced by a prominent writer, it is only fair that its soundness should be analyzed.

The argument is that the score which is accumulated in going game is generally considerably less than 100, averaging not over 60, and that, therefore, the bonus of 100 is more advantageous. The example is given of a pair who adopted these tactics, and on one occasion gathered eight successive hundreds in this manner, eventually obtaining a rubber of approximately 1150 points instead of one of about 350.

The answer to any such proposition is so self-evident that it is difficult to understand how it can be overlooked. It is true that a game-going hand does not average over 60 points, which is 40 less than 100, but a game is half of a rubber. Winning a rubber is worth 250, without considering the 250 scored by the adversaries, if they win. A game, at its lowest valuation, is, therefore, worth 125 plus 60, or 85 more than the 100.

Examining the case cited, it will be seen that even had the pair, who are so highly praised for their self-control in scoring eight hundred before going game, known that for ten successive hands they would hold all the cards, and, therefore, that they had nothing to fear from adverse rubber scores of 250, they, nevertheless, made but poor use of their wonderful opportunities. If, instead of accumulating that 800, they had elected to win five rubbers, they would have tallied at the most moderate estimate five times 350, or 1750, in place of the 1150 of which they boast.

If, however, during that run of luck the adversaries had held two game hands—say, the 5th and 10th, the exponents of self-control would have made on the ten hands about 450 points, instead of approximately 1350, which would have been secured by players who realized the value of a game.

In the event of an even and alternate division of game hands, the non-game winners at the end of twelve hands would have lost three rubbers and won none, as compared with an even score had they availed themselves of their opportunities.

It is, therefore, easily seen that the closer the investigation, the more apparent becomes the absurdity of the doctrine that it is advantageous to sacrifice a game for a score of 100.

2. WHEN THE ONLY OFFENSIVE DECLARATION HAS BEEN MADE BY THE DEALER

In this case the Fourth Hand, before making a declaration in any manner doubtful, should remember that his partner has, by failing to declare, announced that he has not sufficient strength to overbid the Dealer. This does not, however, signify that he has a trickless hand, and the Fourth Hand may even yet count upon him for some support. There are two features—both of importance—one weighing in favor, the other against, a declaration under these circumstances. One is, that the strength being over the Fourth Hand, he is placed in the worst possible position in the play, and there is more probability of his being doubled than under any other conditions. If he be doubled, it is not likely that his partner can take him out or prove of material assistance, as the double is apt to come in the case in which the partner has passed with a practically trickless hand.

On the other hand, the lead is with the partner, and especially when a No-trump has been declared, it may be of great advantage to indicate the suit which should be led. The Fourth Hand should, therefore, if possible avoid placing a large bonus in the adversaries' column, yet he should not hesitate to take a chance when his hand indicates that the lead of a certain suit will be likely to save game.

In the event of a Dealer's declaration which is not apt to produce game coming up to the Fourth Hand, he should pass, unless his holding convince him that he will be able to go game should he declare.

3. WHEN THE ONLY OFFENSIVE DECLARATION HAS BEEN MADE BY THE SECOND HAND

In this situation the Fourth Hand is in much the same position as the Third Hand when the Dealer has made an offensive declaration, and the Second Hand passed.[12] The only difference is that the Fourth Hand knows that both of the adversaries are apparently weak, whereas in the previous case the Third Hand had that information as to only one. The Fourth Hand can, therefore, act much more freely, and should, if in any way possible, increase a declaration which is not apt to result in game to one of the three game-producing bids. At a love score, a Club or Diamond declaration should be allowed to stand in two cases only:—

(a) Weakness, which does not make any further declaration reasonable.

(b) A combination of cards which makes it probable the Club or Diamond call will result in game.

[12] See page 86.

When the Second Hand has declared No-trump, Royals, or Hearts, his bid should be accorded exactly the same treatment that a similar call of the Dealer receives from the Third Hand.[13]

[13] See page 86.

Neither a two nor three Spade declaration made by the partner should under any circumstances, be passed. In these cases, the Fourth Hand can have little doubt what course to pursue. His partner's hand is spread before him almost as clearly as if exposed upon the table.[14] With weakness, or with a moderate hand, he should bid one Royal, this being merely a takeout, and not giving any indication of strength. In this position he is placed in the same situation as the Third Hand when the Dealer has made a similar declaration,[15] and these two propositions are the only instances in the modern game of Auction where a player without strength is required to assume the offensive. No matter how weak the hand may be, the Fourth Hand must declare one Royal, so as to reduce the contract, and also to increase the advantage obtained from its fulfillment. The partner must read "one Royal" to be an indication of weakness, or, at least, not a showing of strength.

[14] See pages 67-72 inc.

[15] See pages 88, 89, 90.

With Spade length or strength, the Fourth Hand, especially in the case of the three Spade declaration, should bid two Royals. If he declare anything but Royals, he says to the partner, "I realize perfectly what you have, but my hand convinces me that the declaration I am making will be more advantageous than the one you have suggested."

In the event of one Spade doubled coming to the Fourth Hand, he is also accurately informed as to his partner's holding, and suggestion.[16] In this case, it is the rare hand which does not warrant an offensive declaration.

[16] See pages 65, 66.

It is not so great an advantage for the Fourth Hand to call two No-trumps over one No-trump declared by the Second Hand as it is for the Third Hand to similarly overbid the Dealer.[17] The reason for this is, that the main purpose of this overbid by the Third Hand is to prevent the Fourth Hand from indicating the suit he desires his partner to lead, but the Dealer, having already declared weakness, is not so likely to be able to make a bid which will in any way interfere with the success of a No-trumper. It is, however, not at all impossible that a declaration of the Dealer's long weak suit, especially when the Second Hand has an honor or two of it, may be awkward for the No-trump declarer, and therefore, with the holding which justifies it, the bid of two No-trumps, under these conditions, is distinctly commendable.

[17] See pages 108, 109.

4. WHEN THE ONLY OFFENSIVE DECLARATION HAS BEEN MADE BY THE THIRD HAND

In this position the Fourth Hand is informed of his partner's weakness. This weakness is probably quite pronounced, as the Second Hand has passed the Dealer's defensive declaration, and although it is doubtless reasonable for the Fourth Hand even yet to count upon his partner for one trick, he certainly would not be justified in expecting much greater aid. It is a place for caution; although he is in the advantageous position of sitting over the adverse strength, he should bid only if he see a fair chance for game, or think his hand is such that he may safely attempt to force the adversary.

5. WHEN THE DEALER HAS MADE A DEFENSIVE, AND BOTH THE SECOND AND THIRD HANDS OFFENSIVE, DECLARATIONS

In this situation, the Fourth Hand comes more nearly within the category of a second round, or late bidder; that is, he is in the position in which a player often finds himself when, after some bidding in which he has not participated, he is in doubt whether he has sufficient strength to advance his partner's declaration.

Under such circumstances, a player should always remember that his partner has counted upon him for a certain percentage of high cards. If he have not more than that percentage, it would be the part of extreme folly for him to declare. When the partner has made a suit declaration, and he has weakness in the suit, but some strength elsewhere, he should be especially careful, and, before bidding, convince himself that his side strength is more than his partner expected. Advancing a partner's suit bid by reason of strength in other suits, while, when the strength warrants it, unquestionably sound, is apt to deceive the partner, as his first thought necessarily is that the bid indicates help in the suit declared.

When the partner has declared No-trump, and the Third Hand has called two in a suit, the Fourth Hand is in much the same position regarding the advancement of his partner's No-trumper as the Third Hand when the Dealer bids a No-trump, and the Second Hand, two of a suit.[18] The only difference is that in this case there is little probability of high-card strength being developed on the left.

[18] See page 111.

6. WHEN THE DEALER AND SECOND HAND HAVE MADE OFFENSIVE DECLARATIONS, AND THE THIRD HAND PASSED

It is an exceptional hand which justifies taking the partner out of a suit declaration, called over a No-trump bid by the Dealer. The partner has the advantage of sitting over the Dealer, while the Dealer would have this same advantage should the Fourth Hand declare some other suit.

In this position the partner having bid two Clubs or Diamonds, the Fourth Hand, with the other three suits stopped, is justified in assuming that the original No-trump was made with the minimum strength, and the chance of game, as the declaration stands, being remote, should try a bid of two No-trumps.

When the Dealer has declared a suit, and the Second Hand, No-trump, the Fourth Hand should overbid the Second with a suit declaration (except, of course, in the almost inconceivable case in which the strength of the Fourth Hand is in the suit named by the Dealer), with the same holding that the Third Hand is justified in overbidding the Dealer's No-trump.[19]

[19] See pages 96-108 inc.

7. WHEN THE DEALER AND THIRD HAND HAVE MADE OFFENSIVE DECLARATIONS AND THE SECOND HAND PASSED

In this case, both adversaries having shown strength, and the partner weakness, it is dangerous for the Fourth Hand to declare, and he should do so only when his holding convinces him that his declaration is not likely to be successfully doubled.

8. WHEN ALL THREE PLAYERS HAVE MADE OFFENSIVE DECLARATIONS

This case is entirely analogous to the second round or late bidding, and is covered under the head of CONTINUATION OF THE BIDDING.



VI

CONTINUATION OF THE BIDDING

After the completion of the first round, the situation of the bidder becomes so complex that it is most difficult to apply general rules. Some principles, however, should be borne in mind.

Bidding one Spade, or passing, places a player with two tricks in a position to increase his partner's call; but when a bidder has already shown the full strength, or practically the full strength, of his hand, he should not, under any circumstances, advance either his own or his partner's declaration. The temptation to disregard this rule is at times exceedingly strong. For example, the dealer declares one Heart, holding King, Queen, at the top of five Hearts, and the Ace of Spades. The partner calls one No-trump, and the Fourth Hand, two Royals. In such case, the original Heart bidder frequently advances the No-trump to two, because he has the adverse suit stopped, without considering that his partner, in bidding one No-trump, counted upon him for either that Ace of Spades, or the equivalent strength, and, therefore, he should leave the question of the continuance of the No-trump to the player who knows its exact strength.

Another example of this proposition may be worthy of consideration. The dealer holds

Spades X, X, X Hearts Ace, X Diamonds King, Knave, Ten, X, X Clubs X, X, X

He bids one Diamond; Second Hand, pass; Third Hand, one Heart; Fourth Hand, one Royal.

In this position a thoughtless player might call two Hearts, but such a declaration would greatly exaggerate the value of the hand. The dealer by his first bid has announced his ability to take at least three tricks if Diamonds be Trump, and at least two tricks if the deal be played without a Trump. His hand justifies such a call, but that is all; having declared his full strength, his lips must thereafter be sealed.

His partner is already counting upon him for two high-card tricks, which is the maximum his hand can possibly produce; should he call two Hearts on the basis of the Ace, the original Heart bidder would expect assistance to the extent of at least three tricks. He might receive only one.

If, however, the dealer's hand be

Spades X Hearts X, X, X, X Diamonds King, Knave, Ten, X, X Clubs Ace, X, X

a very different proposition presents itself. While this combination, had No-trump been called, would not be stronger than the other and should not advance the bid, with Hearts Trump it is a most valuable assistant, and being worth at least three tricks, is fully warranted in calling at least two Hearts.

The fact that it contains four Hearts is one material element of strength and the singleton Spade is another, neither of which has been announced by the original call.

One of the most difficult tasks of the bidder is to accurately estimate the number of tricks the combined hands of his partnership can reasonably be expected to win. It sometimes occurs, especially in what are known as "freak" hands, that one pair can take most of the tricks with one suit declaration, while with another, their adversaries can be equally successful. This is most apt to happen in two-suit hands, or when length in Trumps is coupled with a cross-ruff. In the ordinary run of evenly divided hands, there is not such great difference in the trick-taking ability of two declarations. The player who, except with an extraordinary hand, commits his side to ten or eleven tricks, after the adversaries have shown that with another declaration they do not expect to lose more than two or three, is extremely venturesome, and apt to prove a dangerous partner. In normal deals, a change in the Trump suit does not produce a shift of seven or eight tricks.

WHEN TO ADVANCE THE BID

It is frequently most difficult for a bidder to determine whether he is justified in advancing his own or his partner's declaration, and when in doubt it is generally better to err on the side of conservatism.

The continuation of a No-trump without the adverse suit thoroughly guarded is most dangerous, and should be risked only when the Declarer is convinced beyond doubt that his holding justifies it, or when the partner has shown that he can stop the threatening suit.

When the partner, either as Dealer or Second Hand, has declared one No-trump, the bid has unquestionably been based upon the expectation of average assistance, and unless able to furnish more, a higher call should not be made. If, however, the partner bid twice, without aid, two tricks unquestionably justifies assisting once.

The minimum trick-taking ability with which an original suit declaration is made being appreciably greater than the number of tricks contained in a border-line No-trumper, the former should be assisted with less strength than is required to advance the latter. With two sure tricks the partner's suit call should be helped once by a player who has not declared, but whether a No-trump should be aided with just two tricks and no chance of more is a question depending upon the judgment of the bidder and upon whether one of the tricks is in the adverse suit. With two sure high-card tricks and a five-card suit, but without the adverse suit guarded, the five-card suit is generally the call, especially if two in it will be sufficient. Three Clubs, however, should not be declared without due consideration, as that declaration is recognized as demanding two No-trumps from the partner if he have the adverse suit stopped.

Being void or holding only a singleton of a suit, especially if it be the suit declared by the adversary, is to be considered in reckoning the trick-taking value of a hand which contemplates assisting a partner's Trump declaration. For example, four small Hearts, the Ace and three other Clubs, and five small Diamonds, when the partner has called one Heart, are worth three or four tricks, although the hand contains but one Ace and no face card. Holding such a combination, a partner's bid of one Heart should be advanced at least twice.

When a declaration by the dealer is followed by two passes and an overbid by the right-hand adversary, the dealer is frequently placed in a doubtful position as to whether he should advance his own bid. Some authorities contend that with less than six tricks he should wait for his partner, and while no inflexible rule can be made to cover all such cases, the follower of this proposition has probably adopted the safest guide.

When the original call has been one No-trump, it is the part of wisdom with less than six tricks, even if the adverse suit be stopped twice, to give the partner a chance. If he can furnish more than two tricks, he will declare, and the Dealer can then, if he so desire, continue the No-trump, but to bid without first hearing from the partner is obviously venturesome. If the Dealer have five tricks, that is enough to save game, but is three tricks short of making two No-trumps.

When the Dealer has declared a strong No-trump with one unprotected suit and his right-hand adversary calls two in that suit, it is manifestly unwise to continue the No-trump. Holding six sure tricks in a higher-valued suit or seven in a lower, it is probably wise to bid two or three, as the exigencies of the case may require, in that suit.

In close cases, when advancing or declining to advance the partner's bid, the personal equation should be a most important, if not the deciding, factor. Some players are noted for their reckless declaring; with such a partner the bidding must be ultra-conservative. Other players do not regard conventional rules in their early declarations. The bids of a partner of this kind should not be increased unless the hand contain at least one trick more than the number that normally would justify an advance.

When playing against a bidder who has the habit of overbidding, full advantage should be taken of his weakness, and whenever possible he should be forced to a high contract he may be unable to fulfil.

When a dealer who has opened with one Spade, or any other player who has passed the first round, subsequently enters the bidding, he gives unmistakable evidence of length but not strength. This is a secondary declaration, and the maker plainly announces, "I will take many more tricks with this suit Trump than any other; indeed, I may not win a trick with any other Trump."

Overbidding a partner's secondary declaration, or counting upon it for tricks when doubling an adversary who has overcalled it, shows inexcusable lack of understanding of the modern system of declaring.

WHEN TO OVERBID THE PARTNER

Overbidding a partner with a declaration which he has once taken out is only authorized by an honor count which is of material value, or a sure game. For example, if a player declare one Royal, holding four or five honors, and the partner overbid with a No-trump, the original declarer should bid two Royals; but without the big honor count it is wiser to let the No-trump stand, as the partner has announced weakness in Spades.

The same line of reasoning should be followed when the partner has called two of a suit over a No-trump. As a rule, under these conditions, it is most unwise for the original No-trump declarer to bid two No-trumps, but with four Aces, the value of the honors thoroughly warrants such a declaration, unless the partner's call has evidently been a "rescue."

The "rescue" or weakness take-out is a warning not to be disregarded. Two Clubs or Diamonds over a No-trump is the most self-evident example, and after such a call by the partner it takes a holding of eight sure tricks to justify two No-trumps. Of course, with four Aces, seven tricks would warrant the call, on the theory that at the worst the 100 for the Aces would set off the possible loss by the double, and more than equal the loss if a double be not made.

FLAG-FLYING

The practice generally called "flag-flying" consists in overbidding an adverse declaration, which will surely result in game and rubber, with a holding which is not of sufficient strength to carry out the contract.

While at times flag-flying is of great advantage, in inexperienced hands it is apt to prove a dangerous expedient. The argument in its favor is obvious. The bonus of 250 points for the rubber really makes 500 points the difference between winning and losing, and in addition there must be computed the points and honors which would be scored by the adversaries in the deal with which they go game, and the points and honors which may be scored by the flag-flyers in the succeeding deal which they hope will carry them to their goal. On this basis flag-flyers estimate that it makes a difference of 600 points whether their opponents go out on the current deal or the flag-flyers score game on the next, and they claim that any loss under 600 is a gain. The estimate is correct; the claim, ridiculous. Whenever the next deal furnishes the player who offers the gambit sufficient strength to capture the rubber, he gains, when his loss has been under 600, but at best it is not more than an even chance that he will win, and when the pendulum swings in the adverse direction, the only result of the performance with the flag is to increase the size of the adversaries' rubber by the amount of the sacrifice. This continued indefinitely is bound to produce Auction bankruptcy.

The player who figures that, on the doctrine of chances, he and his partner will hold the strong cards once in every two deals, should remember that the fickle goddess would never have deserved nor received her well-earned title had she been even approximately reliable.

A run of bad luck may continue for an indefinite period. It has pursued good players not only for a day or a week, but continuously for months and years. It does not sound warnings announcing its appearance or disappearance. To attempt to fight it by the flag-flying process as a rule only multiplies the loss many fold. And yet, it must not be understood that the flag-flyer should always be shunned and condemned. When his loss amounts to only 100 or 200, or when, not detecting his purpose, the adversaries fail to double, and the loss is, therefore, smaller, the odds favor his exhibition of nerve. Flag-flying, however, is like dynamite: in the hands of a child or of one unfamiliar with its characteristics, it is a danger, the extent of which none can foretell; but used with skill, it becomes a tool of exceptional value.

It is only during the rubber game that even the most enthusiastic and expert flyer of the flag should allow it to wave. With a game out, to make the play successful Dame Fortune must bestow her favors twice in succession. Before taking such a long chance, a player should realize that there are future rubbers which he has an even chance of winning, and that it is better to minimize the present loss than to allow it to become so great that, even if good fortune follow, it will be impossible to recoup. On the first game of the rubber, or with a game in, and the adversaries still without a game, it is plainly too early and the situation is not sufficiently desperate to resort to any real flag-flying. Except when playing the rubber game, a voluntary loss of over 100 should never be considered.



VII

DOUBLING

All doubles, except the double of one Spade by the Second Hand, which is really an informatory bid,[20] are made for the purpose of increasing the score of the doubler.

[20] See pages 65, 66.

The old idea of informatory doubles has been abandoned. Now when a player doubles, he does not invite a No-trump by showing one or more tricks in the adversary's suit, but he practically says, "Partner, I am satisfied that we can defeat this declaration, and I desire to receive a bonus of 100 instead of 50 for each trick that our adversaries fall short of their contract. I do not wish you to overbid, unless your hand be of such a peculiar character that you have reason to believe the double will not be very profitable and feel sure that we can go game with your declaration."

Although doubles are made under widely divergent conditions, they may be subdivided into two classes:—

1. The double of a declaration which, if successful, will result in game, regardless of the double, such as four Hearts, with a love score.

2. The double which, if unsuccessful, puts the Declarer out, although if undoubled, he would not secure the game by fulfilling his contract, such as two or three Hearts, with a love score.

In the first instance, the doubler has nothing to lose except the difference in points which the Declarer may make as a result of the double. When, for example, a bid of four Hearts is doubled and the Declarer fulfils his contract, the double costs exactly 82 points. If the Declarer fall one trick short, the double gains 50 points. When, however, there is a redouble, the loss is increased 114 points, the gain 100 points. The doubler is, therefore, betting the Declarer 82 to 50 that he will not make his contract, and giving the Declarer the option of increasing the bet, so that the odds become 196 to 150. It is evident, therefore, that even when the Declarer will go out in any event, it is not a particularly advantageous proposition for the doubler to give odds of 8 to 5 or 20 to 15, if the chances be even. When the declaration is Royals or No-trumps, the odds against the double are increased. If four No-trumps be doubled, the figures are 90 to 50 with the option given to the Declarer to increase them to 220 to 150.

The explanatory remark so often heard after an unsuccessful double, "It could not cost anything, as they were out anyhow," is not an absolutely accurate statement. It may be worth while to consider one ordinary illustration of how many points may be lost by a foolish double of this character. A bid of four Hearts is doubled and redoubled. The Declarer takes eleven tricks, as he is able to ruff one or two high cards which the doubler hoped would prove winners. This is an every-day case, but the figures are rarely brought home. Without a double, the Declarer would have scored 40 points; with the redouble, he scores 160 points and 200 bonus, or 360, presented by an adversary, who hoped at most to gain 50 and thought his effort "could not cost anything."

A doubtful double should not be made when the partner has another bid, as, for example, when the adversary to the right has called four Hearts, over three Royals declared by the partner. Under these circumstances, the double, on the theory that the doubler expects to secure a large bonus, may properly deter the partner from a successful four Royals declaration. Even when the double is successful to the extent of 100, that is not a sufficient compensation for losing the opportunity to win the game.

The fact that a good player has declared an unusually large number of tricks, as, for example, five Hearts, is not in itself a reason for doubling. A player of experience, when he makes such a declaration, fully realizes the difficulty of the undertaking. He does not take the chance without giving it more consideration than he would a smaller bid, and it is only fair to assume that he has a reasonable expectation of success. Doubling, therefore, merely because the bid requires ten or even eleven tricks, is folly, pure and simple. This comment, however, does not apply when the bid is of the flag-flying character.[21] As to whether or not it comes within that category the doubler will have to determine. The Auction expert is always on the lookout for an opportunity to gather a large bonus at the expense of a flag-flyer, and as unduly sanguine players indulge in that practice more than others, their declarations should be subjected to the most rigid scrutiny.

[21] See pages 139-142 inc.

The doubtful double, which, should it prove unsuccessful, will result in the Declarer scoring a game he would not otherwise obtain, is, as a rule, inexcusable. By this is not meant that a bid of two or three Hearts or Royals, or of three or four Clubs or Diamonds, should never be doubled. That would be absurd doctrine, but such a double should never be made with the chances even, or nearly even. An experienced bidder will not risk presenting the adversaries with the game and a bonus unless reasonably sure of defeating the declaration.

Another absurd notion is doubling because of the partner's general strength. The partner has an equal opportunity to double, and is much better posted in relation to his own cards. If the strength be his, he should decide whether or not to take the chance. When, however, one partner has some strength in the suit the adversaries have declared, and the other, high side cards, the double is more apt to confuse the Declarer if made by the player without the Trump strength.

The above refers to doubtful doubles only; when the indications are that the Declarer can be decisively defeated, the double is most important. It is worth 100 if the Declarer go down two; 150, if he lose three, etc. These additional points should not be allowed to escape.

Even the most venturesome doublers realize that, except in the unusual case, it is unwise to double a bid of one, whether it be in a suit or No-trump. Some players hesitate about doubling a bid of two, preferring to take the chance of forcing the bidder higher. No general rule covering the situation can be laid down, as it depends greatly upon the character of the doubler's hand whether the adversary is apt to advance his bid.

A double of a No-trump is much safer than of a suit declaration. The doubler of the No-trump knows approximately what to expect from his long suit, what suits he has stopped, and if one be unguarded, can estimate how many tricks it may be possible for the declarer to run. The doubler of a suit declaration cannot figure with any such accuracy. He rarely has more than two winning Trumps, and therefore, as a rule, must depend upon side Aces and Kings for the balance of his tricks. It is always possible that the Declarer or his partner may be absolutely void of the suit or suits in which the doubler expects to win his tricks, so that sometimes a hand with which the most conservative player would double, goes to pieces before a cross-ruff. When one hand is evenly divided, the chances are that the others are of the same character, but it is not a certainty that they are. When one hand has a very long suit, and is either blank in some other suit, or has but a singleton of it, the other hands are apt to contain very long and very short suits. Therefore, if the doubler be without, or have but a singleton of, a suit, he should be more conservative, in doubling a suit declaration upon the expectation of making high side cards, than when he has an evenly divided hand.

Probably the most advantageous situation for a double is when the partner has declared No-trump, and the adversary to the right, two of a suit, of which the doubler, in addition to other strength, holds four cards, at least two of which are sure to take tricks. This comes nearer being an informatory double than any other in vogue in the game of to-day. The partner, however, should not take it out unless his No-trump consist of some such holding as a solid suit and an Ace.

A hand of this character may not prove formidable against a suit declaration, and it justifies the original Declarer, as he knows that the adverse suit is well stopped, in bidding two No-trumps. It is one of the few cases where it is not advisable to allow the double of a partner to stand.

It is generally conceded that the double, although a most powerful factor in the game, and the element which is productive of large rubbers, is used excessively, especially by inexperienced and rash players. If a record could be produced of all the points won and lost by doubling, there is little doubt that the "lost" column would lead by a ratio of at least two to one.

The double in the hands of a discreet player of sound judgment is, indeed, a powerful weapon greatly feared by the adversaries; when used by the unskilled, it becomes a boomerang of the most dangerous type.

A player cannot afford to have the reputation of never doubling, as that permits his adversaries to take undue liberties in bidding, but it is better to be ultra-conservative than a foolish doubler who continually presents his opponents with games of enormous proportions. A player should not double unless able to count with reasonable exactness in his own hand and announced by his partner a sufficient number of tricks to defeat the Declarer. It is not the place to take a chance or to rely upon a partner, who has not shown strength, for an average holding. It must also be remembered as an argument against a doubtful double that the Declarer is more apt to make his declaration when doubled, as he is then given more or less accurate information regarding the position of the adverse strength, and can finesse accordingly. A double frequently costs one trick—sometimes even more.

THE CHOICE BETWEEN A GAME AND A DOUBLE

A most interesting question arises when a player is placed in the gratifying position of having the opportunity of electing whether to go game or secure a bonus by doubling.

Which course he should take depends entirely upon the state of the rubber, and the size of the bonus that the double will probably produce. A game is always to be preferred to a double which is not apt to net more than 100. When 200 is sure and a greater bonus probable, the double should be made during either the first or second game of the rubber. During the rubber game, however, the doubler should be more conservative, and should "take in" his rubber unless satisfied that the double will produce 300, with a potential possibility of more.

The reason, which may not at first be apparent, for this difference in the situation, may be briefly explained as follows: Before a game has been won, the securing of a large bonus in the honor column places the fortunate doubler in a most advantageous position, as he starts the rubber insured against loss unless he suffer a similar penalty.

When the only game finished has been won by the adversaries, a large bonus should be preferred to game. As the adversaries already have a game, the next hand may give them the rubber, and should it do so, its amount will be most materially affected by the action of the player who has the chance either to score a bonus or win a game. If the first game be of normal size, a large bonus will nullify the result of the rubber, but if instead a game be taken in the adversaries will score an average rubber.

When the player considering a double has a game and the adversaries have not, he is in a most excellent position to double with the hope of a big winning. To secure the enlarged rubber, it is only necessary for him to obtain one game before the adversaries get two, and as the odds are greatly in his favor it is a chance worth taking.

When, however, each side has a game and the question is whether to obtain a bonus or score rubber, the bonus must be large and sure to justify giving up a rubber practically won for merely an equal chance of capturing a larger one. It has been elsewhere stated that when a player who has an opportunity to win a rubber fails to avail himself of it, and on the next hand the adversaries reach the goal, the loss may be roughly estimated at 600 points. The player who doubles during the third game knows that the next hand may see the adversaries score the rubber. Even if he obtain 400 points by doubling, and this happens, the adversaries gain to the extent of approximately 200 points by his action. On the other hand, he has an equal chance for the game, and if he win it, he will be the gainer by the amount secured by the double. When he has a sure 400 in sight, or even a sure 300, with a reasonable chance of more, the odds favor the double, but it is the height of folly to take an even chance of losing 600 unless 300 be the minimum return.

Advice as to whether to double or go game is useful only for players who can with accuracy estimate the trick-taking value of their hands. To refuse a double which would net several hundred for the sake of going game and then fall a trick short of both the game and the declaration is most exasperating, while on the other hand to double for a big score, instead of taking in a sure game, only to have the double fail, is equally heart-breaking.

The player who takes either horn of this dilemma must be sure of his ground and must figure the chances with the greatest care.

WHEN TO REDOUBLE

The question of when to redouble is so intricate that it is hard to consider, except when the specific case arises. Some players frequently redouble, as a kind of bluff, when convinced their declaration will fail, the intent being to frighten either the doubler or his partner into another declaration. Against a very timid player, this is sometimes successful, but unless it catch its victim, it is expensive bait.

Nine out of ten redoubles, however, are bona fide, and made because the fulfilment of the contract seems assured. Even then, however, a player should not redouble unless practically positive that neither of his adversaries can get out of the redouble by making a higher bid.

The player who has been doubled and is sure of his contract is in a most enviable position; game and a handsome bonus both are his, and it would be most foolish for him to risk so much merely for the chance of the extra score. If, however, there be no escape for the doubler, the redouble is most valuable, and a real opportunity for it should never be overlooked.

WHAT TO DO WHEN THE PARTNER IS DOUBLED

The player who, whenever his partner's declaration is doubled, becomes frightened, concludes that the worst is sure to happen, and that it is his duty to come to the rescue by jumping headlong into some other declaration, even if it require an increased number of tricks, is a most dangerous vis-a-vis. A double does not justify the assumption that the Declarer is beaten, especially when the partner has any unannounced help. If the partner be weak, it is folly for him to go from bad to worse; if strong, he may enable the Declarer to make a large score. In any event, in nine cases out of ten, "standing pat" is his best policy.



VIII

LEADING

The selection of the correct lead in Auction is not attended with so many difficulties as in Whist, or even in Bridge. In Whist, the original leader is obliged to begin the play in the dark, the turn-up constituting his entire knowledge of the strength or weakness of the other players. In Bridge, the extent of his information is limited to the inferences that can be drawn from the declaration and the double, but in Auction every player has made at least one announcement which is more or less instructive.

When there has been considerable bidding it is frequently possible to accurately estimate the length and strength of the suit of each player and the trick-taking value of the balance of his hand. When only one or two declarations have been made, so much information may not be obtainable, but even then the leader, from the failure of certain players to bid, may be able to make deductions of considerable value.

The Auction leader, therefore, must remember the various declarations, draw both positive and negative inferences therefrom, and whenever it is not advisable to open his partner's suit or his own, should follow the old principle which, since the days of Pole, has been applicable to all games of the Whist family, and realize "'Tis seldom wrong to lead up to the weak and through the strong."

The original opening is materially varied by the character of the final declaration, the system of leading against a No-trump being quite different from that employed when a suit is Trump.

HOW TO LEAD AGAINST A NO-TRUMP

When the partner has not shown strength, the leader, against a No-trump, should open his own long suit. If he have two long suits, he should pick the stronger except when he has declared it, and has not received support from his partner, in which case it is generally wise to try the other. The possible exception to the lead of a long suit against a No-trump is when that suit has been declared, has not been helped by the partner, and the No-trump has been subsequently bid to the right. In this situation, with a tenace in the long suit, it is sometimes advisable to try, by leading another suit, to get the partner in, so that he may lead through the Declarer's strength in the suit called by the leader. This, however, is a dangerous expedient when the partner has not declared. Should a suit be guessed which the partner cannot win, one of his high cards is apt to be sacrificed, and not only nothing gained, but the advantage of the lead transferred to the adversary. If two high cards be missing from the tenace suit, as in the case when it is headed by Ace, Queen, Ten, or King, Knave, Ten, and the Declarer hold the missing honors and one small card, it will take two leads to establish the suit. It is not likely that a partner without sufficient strength to declare will be able to get in twice, and trying to put him in once is most apt to establish a suit for the Declarer. Therefore, as a general proposition, unless the partner have declared, the tenace suit should be led. When, however, the partner has shown a suit, opening it, in preference to a tenace, is elementary and compulsory.

When the partner has declared, the leader should open the suit named unless satisfied that his own affords a more potent weapon for the attack.

There are only three conditions which justify the leader in assuming this, viz.:—

(a) When the leader has called his suit and his partner has advanced the declaration.

(b) When the leader's suit is headed by Ace, King, Queen, or King, Queen, Knave.

(c) When the leader has only a singleton of his partner's suit and has several reentries.

Innumerable tricks, games, and rubbers have been thrown away by a leader who, considering solely his own hand, has started with his suit in preference to that of his partner. There is some peculiar characteristic in the composition of many players which magnifies the value of their own cards, so that they seem of greater importance and more desirable to establish than their partners'. Even experienced players have been known to commit such an Auction absurdity as opening a suit headed by a Knave, in preference to the suit named by the partner, which, of necessity, contains the strength requisite for a Trump declaration.

It is fair to estimate that ten tricks are lost by denying the partner's declaration to one that escapes the player who leads his partner's suit in preference to his own.

When the partner has declared, his suit can be counted upon for both length and strength, and unless it be practically solid, his hand contains at least one reentry. The leader by his opening can attack only one-quarter of the No-trump fortification, and it is his duty to pick out the spot which promises to be most vulnerable. A No-trump call is very likely to spell game unless a suit can be established against it. In order to accomplish this it is generally necessary to start with the first card led. Therefore, making the right original opening is probably the only opportunity to save the game. When the leader selects his own suit in preference to his partner's, he should be able to say, "In spite of the strength you have declared, I am reasonably sure that we have a better chance to establish this suit than yours."

As a rule, however, the leader does not have sufficient strength to support such a statement, and, therefore, his lead generally says, "Partner, I know you have considerable strength, you may have declared expressly for the purpose of asking me to lead your suit, but I selfishly prefer to play my own hand rather than act for the benefit of the partnership."

It is but a puerile excuse for a leader who does not open his partner's suit to explain that the No-trump was called by the right-hand adversary after the partner's declaration, and that the bid, having been made with the anticipation that the suit named would be led, he should surprise the Declarer. It is true that the Declarer expects that suit, but it may be the only opening he fears. It is more than possible that the suit is stopped but once, and that leading it will save the game, even if it do not defeat the declaration. It is certainly a very short-sighted or unduly sanguine player who selects a suit of his own, which has not nearly the strength of his partner's, merely on the wild chance that his partner, rather than the No-trump bidder, has the missing high cards.

When the partner has declared two suits and the leader has length or strength in one of them, he should open it, but when he cannot assist either, he should open the suit named first, as it is probably the stronger.

As will be seen from the tables of leads against a No-trump declaration, in some cases whether the leader has a reentry materially affects the manner in which he should open his long suit. By a reentry in this connection is meant either an Ace or King, unless the suit containing the King have been bid by the adversary to the left of the leader. In that case the King cannot be expected to win unless accompanied by the Queen. A Queen, or even Queen, Knave, cannot be considered a reentry, as the suit may not be led three times.

The reason for varying the lead, depending upon the presence of a reentry, is that the sole thought of the leader against a No-trump is to establish the suit led, and to insure so doing he opens his suit exclusively with that end in view, regardless of whether it would otherwise be the opening most apt to prove trick-winning. He knows that the Declarer will, if possible, hold up a winning card until the Third Hand is unable to return the suit. Therefore, if he be without a reentry, he must do all in his power to force the winning card from the adversary's hand as early in the play as possible. If he have a reentry, he may play much more fearlessly. An example of this is a long suit, headed by Ace, Queen, Knave. The most advantageous lead from this combination is the Ace (as an adversary may hold an unguarded King), and that would be the lead with a reentry; but the chances are that the partner does not hold more than three cards of the suit, and, if it be opened in the usual way, the King will be held up until the third round. The leader without a reentry, therefore, is compelled to open with the Queen, so as to establish the suit, while the partner, who probably has a reentry, still retains a card of it.

Another important convention which applies to the opening of the leader's suit against a No-trump declaration (but, of course, against a No-trump declaration only) is that the original lead of an Ace calls for the partner's highest card. An Ace, therefore, should be led from such a combination as a suit headed by Ace, King, Knave, Ten, since the drop of the Queen will permit the suit to be run without hesitation, and the failure of the partner to play the Queen will permit the leader to place its position positively, and to continue the suit or not, as his judgment and the balance of his hand dictate. This doctrine is extended to all cases of the original lead of an Ace against a No-trump declaration.

The Ace should not be led unless the partner's best card, regardless of its size, be desired, and the partner should play it unhesitatingly, be it King, Queen, or Knave, unless the Dummy convince him that meeting the demand of the lead will be trick-sacrificing, in which case the leader's command should be ignored.

In leading a partner's suit, the general rule of selecting the fourth best, when opening with a small card, is not followed. The object in leading that suit is to strengthen the partner, and it is more important to do that and also to tell him what is the leader's highest card than to post him regarding exact length. Holding either two, three, or four of a partner's suit, the top, therefore, should be led, followed on each succeeding trick by the next in order, the lowest being retained until the last. This is sometimes called the "down and out." The one exception to the lead of the top of the partner's suit is when it consists of three or more headed by Ace or King, and the right-hand adversary has called No-trump after the suit has been declared. In that case, it may be that the stopper which the Declarer thinks he has in the suit can be captured, and the lead, therefore, should be a low card.