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 cla.s.ses:--

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 ill.u.s.tration 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 circ.u.mstances, 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 a.s.sume 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 a.s.sured. 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 a.s.sumption 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