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370

BRIDGE

have the right of redoubling, thus making each trick worth four times as much as at first. The declarer has the first option. The other side can again redouble, and so on. It is well to limit the value to which a trick can reach to 100 points. In the play of the hand the laws are nearly the same as the laws of whist, except that the dealer may expose his cards and lead out of turn without penalty. Dummy cannot revoke. The dealer’s partner may take no part in the play of the hand beyond reminding the dealer when it is his lead or dummy’s, and guarding him against revoking. Advice to Players. In the choice of a suit two objects are to be aimed at: first, to select the suit in which the combined forces have the best chance of making tricks; secondly, to select the trump so that the value of the suit agrees with the character of the hand, i.e., a suit of high value when the hands are strong and of low value when very weak. As the deal is a great advantage it generally happens that a high value is to be aimed at, but occasionally a low value is desirable. The task of selection should fall to the hand which has the most distinctive features, that is, either the longest suit or unusual strength or weakness. Xo consultation being allowed, the dealer must assume only an average amount of variation from the normal in his partner’s hand. If his own hand has distinctive features beyond the average, he should name the trump suit himself, otherwise pass it to his partner. It may here be stated what is the average in these respects. As regards the length of suit, a player’s long suit is rather more likely to be fewer than five than over five. If the dealer has in his hand a suit of five cards including two honours, it is probable that he has a better suit to make trumps than dummy; if the suit is in hearts or diamonds, and the dealer has a good hand, he ought to name the trump. As regards strength, the average hand would contain ace, king, queen, and knave or equivalent strength. Hands stronger or weaker than this by the value of a king or less may be described as featureless. If the dealer’s hand is a king over the average, it is more likely than not that his partner will either hold a stronger hand, or will hold such a weak hand as will counteract the player’s strength. The dealer would not, therefore, with such a hand declare no trump, especially as by making a no-trump declaration the dealer forfeits the advantage of holding the long trumps. The following is a rough method of calculating the value of the player’s chances :—Count each ace (above or below the player’s share, 1 ace) as worth 1{- tricks; each king, f trick; each queen, b trick; each knave, l trick; each trump beyond 3|, 1 trick. The result, multiplied by the suit value, gives the player’s net expectation after deducting the value of the adversaries’ chance. As regards the score for honours, compared with an average declaration with 2 honours, 3 honours are equivalent to half an extra trick, 4 honours to 2 extra tricks, and each honour short means a loss of half a trick. In no-trump declarations the value of high cards is nearly double that given above for suit declarations. When the decision has been left to dummy,..he knows that he can expect less than average assistance from the dealer’s hand. On this account he should deduct 1 trick for a no-trump, heart, or diamond declaration. When considering the strength of a hand, account must be taken whether the high cards are guarded or not; a king single is of less value than a queen guarded. Declarations by Dealer.—A hand, to be strong enough for a no-trump declaration, should be a king and knave, or two queens above the average, or a king above the average, if all the honours are well guarded ; and per-

haps even a queen above the average if all the suits are protected. But in doubtful cases a suit of 6 red cards with 2 honours, or even 4, all honours, is to be preferred. With an average hand declare 5 hearts with 2 honours, or 4 with 3 honours; 5 diamonds with 3 honours, or 4 all honours; 6 clubs with 3 honours, or 5 with 4 honours; 8 spades. With a weak hand, containing a king only, or a queen and knave, declare any suit containing 5 cards with 2 honours. With a very weak hand, containing no card higher than a 10, declare 6 hearts or 5 diamonds, or 4 clubs or 1 spade. Hands containing a suit headed by a .strong sequence of high cards lend themselves especially to no-trump declarations. With an established black suit of 5 or 6 cards the dealer should declare no-trump if he has another suit protected. When very weak in red suits the dealer should propose rather more often, especially when blank in a suit. Thus with no hearts he should be content with 1 trump fewer in clubs and 2 trumps fewer in spades than when he has a fair suit of hearts. Declarations by dummy.—When the dealer has passed the declaration to his partner, the latter knows that the dealer’s hand is not strong, either as regards high cards or in the two red suits, whilst there is a slightly increased possibility of the dealer being strong in the black suits. This is about accurately represented by subtracting 1 trick in the case of a no-trump or red suit declaration. With the advantage of the long trumps, the dealer’s side generally have still the better chance of winning the odd trick, and the cautious policy often adopted is a mistake. The value of dummy’s chance, with different declarations, can be calculated by the method given above, and the best chosen. With a hand an ace above the average, or with 3 aces, no trumps should be declared, unless dummy has a suit of 6 hearts or diamonds. With a hand two queens above the average no trump should also be declared, unless there is a good red suit; and there are hands in which all suit declarations are so weak that a no-trump declaration can be made with a king above the average. With an average hand the best suit should be declared, if it consists of 5 cards. If there be no suit of 5 cards, it is sometimes better to declare 3 clubs or spades than 4 of a red suit. With a hand an ace below the average, a red suit should not often be selected unless it contains 6 cards; 4 clubs or 3 spades should be chosen in preference to a suit of 5 hearts or diamonds. Doubling.—When either the dealer or his partner has declared no trumps, hearts, or diamonds, he is nearly certain to have a hand apparently worth two tricks above the normal; the average value of hands will probably be three tricks. It would appear to be to the adversaries’ advantage to double whenever one of them holds a hand with a better face-value than the average strength that the declarer may be presumed to hold. But it has to be considered, first, that doubling gives the declarer a chance of redoubling should he hold an exceptionally strong hand; secondly, that doubling gives information to the dealer— not of much value when the doubler is on the declarer’s left, but of great value when he is on the declarer’s right. The player on the declarer’s left is justified in doubling if the face-value of his hand is 4 tricks above the normal, by the method explained above. In order that the player on the declarer’s right may be justified in doubling, his hand must be considerably stronger, or else his hand must be so free from tenaces that it is immaterial on which side the strength lies. A spade declaration can be much more freely doubled by either player. The presumption is that when the dealer declares spades his weakness fully counterbalances the advantage of the deal. When the dealer has declared spades, either adversary possessing a hand worth