Chapter IV: Introduction (3)

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