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 pa.s.sed.

7. When the Dealer and Third Hand have made offensive declarations, and the Second Hand pa.s.sed.

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 circ.u.mstances, 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 a.s.sure him that one or more of them is either unduly cautious, has pa.s.sed by mistake, or is trying to deceive. If the strength be with his partner, it may be that, by pa.s.sing, 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 pa.s.s, 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 pa.s.s 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 pa.s.s, 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 a.n.a.lyzed.

The argument is that the score which is acc.u.mulated 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 acc.u.mulating 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 circ.u.mstances. 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 a.s.sistance, as the double is apt to come in the case in which the partner has pa.s.sed 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 pa.s.s, 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 pa.s.sed.[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 circ.u.mstances, be pa.s.sed. 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 a.s.sume 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 p.r.o.nounced, as the Second Hand has pa.s.sed 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 partic.i.p.ated, he is in doubt whether he has sufficient strength to advance his partner's declaration.

Under such circ.u.mstances, 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 Pa.s.sED

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.