Chapter 7

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.