The Informatory Double

An Analysis of the Exact Strength Required to Double a One-Trick Bid

R. F. FOSTER

PROBLEM LXXXVIII

Hearts are trumps and Z leads. Y and Z want seven tricks. How do they get them? Solution in the November number.

THE basic idea of the double, when used conventionally, is to provide an outlet for hands which, though they have no long game-going suit, still boast of two (or more) four-card suits. (If the hand or the suit is strong enough to justify bidding a fourcard suit on its merits, there is no need for the double, but such bids must be prepared to find the partner with only the normal support, three trumps.)

It is when these four-card suits are not good enough to bid on their merits, but would be good bids if it were certain that the partner had at least four cards of the suit, that the conventional double comes into service by finding out which suit it is that will fulfil this condition.

If second hand can, by means of the conventional double, get his partner to name a fourcard suit of which the doubler has four himself, the resulting combination of eight trumps, equally distributed between the two hands, is a decided advantage, because either hand can ruff a suit without weakening the other hand.

Experienced players find that eight trumps, divided four and four, between declarer and dummy, are better than if they are distributed five and three, because it may be necessary to lead trumps three times to exhaust the adversaries, which will exhaust the dummy's trumps at the same time. On the other hand, if the trumps are divided four and four, three leads will still leave a trump in each hand.

The ideal doubling hand is one that contains one or more of the doubled suit and four cards of each of the three other suits, so that no matter which suit the partner picks in answer to the double, the resulting combination is the fourfour distribution of the trump suit, but unfortunately hands in which the doubler holds exactly four cards in three suits or five in one and four in each of two others are not common.

THERE are two types of hand which are good doubling propositions, although the suit distribution be uneven. One is a hand in which only one answer will meet the wishes of the doubler, or either of two. If there are two chances, it might be said to be two to one that the answer would be favourable.

The point for the doubler is to be ready to rebid his hand if the answer to his double does not suit him. Here is an example of this type of doubling hand:

Z, the dealer, bids a spade, and the second hand doubles. He has two chances out of three, as either of the red suits will fit his hand. If his partner answers with a bid of two clubs, which is not good enough to give any prospect of game, the doubler is ready to shift to his own suit, diamonds, without increasing the contract. The fear is that the club answer may be on four small cards.

In this case the doubler is fortunate in finding his partner with four cards in a major suit, in which he is able to win the game. After one spade lead the dealer shifted to a small club, and the finesse of the jack held. Two rounds of trumps disclosed two winners in one hand against the declaration, which would have brought in all the spades, so the declarer shifted to the forcing diamonds. After trumping a diamond and leading a winning trump, there was still a trump left in each hand, and this won the game. Give the declarer five trumps and the doubler three, and they cannot go game.

The next question is what to do with hands that have no strong suit in reserve for a rebid, and have not four cards in three suits. The safe rule to give the beginner is not to double without at least two honours in each of the three suits, other than the one doubled; but "honours" have a very variable value, and some more definite scale of values is necessary for sound doubling.

The general book rule is that the strength of the hand as a whole should be about what would justify a third-hand no-trumper, which is five tricks, distributed among the three suits. It would be safer to qualify this by saying that at least one of the two honours in a suit should be better than the queen, and that there should be two honours in each suit, such as ace-queen, king-queen, or king-jack.

I am indebted to Mr. Robert S. Hale, of Boston, for some rather interesting calculations which were made with a view of determining, more accurately, the proper strength necessary for a double. He bases his premises on the theory of suit distribution, a theory which originated with Eli Culbertson, who was captain of the team that won the championship of the United States at the American Whist League congress at Chicago in June. If the first bidder has a long suit and a short one, the chances are that the adversaries also have a long suit. If he has touching honours, the chances are that they also have touching honours; and if his honours are not touching, there is a probability that those against him are the same.

Mr. Hale finds one of the chief values of the double by the second hand, which is not noted by writers on the game, is to keep the bidding going until he gets another chance at it. But he insists that the second hand should not start anything by doubling unless the chances are that he and his partner together have more than average strength as compared to the dealer and his partner. This means strength in high cards, as length in suit suggests that the opponents also have length in some other suit.

DOUBLING STRENGTH REQUIRED

IF we consider the high cards as A K Q J, of which there are 16 in the pack, an average would be one-fourth of these, or 25%. If we consider that the dealer must have at least average strength, and is entitled to some share of the strength outside his bid, we must credit him with an initial bidding value of 25 % of the high cards. This accounts for 50% if the doubler also has 25%. The remaining 50% is then to be distributed between the third and fourth hands with thirteen cards each, and the nine cards that fill out the hand of the first bidder.

This gives us 35 cards, or the fraction 50/35% for each card, so that the chances for the doubler's partner are 13 X 50/35, or 18%. Add this to the doubler's 25%, and if he doubles on an average hand the chances are that he and his partner hold only 43%, against the 57% held by the first bidder and his partner, which is a very poor chance upon which to start a rumpus, as Mr. Hale calls it. The moral of this calculation, to begin with, is not to double on average hands.

We now come to what would be a good doubling hand.

If the doubler holds 35% of the high cards, and the first bidder is credited with at least 25%, we have only 40% to be distributed among the 35 cards already referred to, and the doubler's partner should hold, on the average, 13 X 40/35ths, or nearly 15%. Add this to the doubler's 35%, and we get 50%, which is an even chance, but without any advantage.

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From this Mr. Hale argues that, unless the doubler has more than 35% of the high cards, he is starting a rumpus with the chances all against his getting a game-going bid out of it. The next step, therefore, is to decide just what 35% means, when translated into a hand of aces, kings, and queens.

If we take the Robertson rule as an example, counting the ace as 7, king 5, queen 3, jack 2, and ten 1, the total value of the pack is 72, and the average is 18. This is the theory upon which the Robertson rule is based. To bring a hand up to 35%, when 25% is average, we want it to count 26, which is an ace, or its equivalent, above average in high cards. The Pinch System of valuation, recommended by Mr. Bryant McCampbell, chairman of the Committee on Laws at The Whist Club, is to count aces 4, kings 3, queens 2 and jacks 1. An average hand is therefore 10, and to get 35% we want it to count 14, which is just ace above average. On the double valuation system the average is 3¾ tricks, and 35% of the pack would be 4½ j on the double valuation 9.

The fact that the dealer usually has more than average strength must be allowed for, and the second hand should be correspondingly stronger to make the double both safe and remunerative. Suppose the dealer holds an average of queen above average, the second hand should have an ace AND QUEEN above average to justify the double and the expectation of getting anything worth while out of it. If a dealer is known to refrain from bidding unless he holds at least a king above average, second hand should have ace AND KING above average to justify a double.

The point for the doubler to keep in mind is that he is gambling on his partner having more strength than the dealer's partner if the double is to produce a game-going bid. If there is more strength in the hand of the dealer's partner, the double will not produce enough points to offset what might have been gained in penalties by passing and playing to defeat the contract.

Another point that is often overlooked is that the double lets the third hand out of the responsibility of taking the dealer out of a dangerous contract when the third hand has only one or two small cards of the dealer's suit.

In such cases, both the doubler and the third hand being short in the suit named by the dealer, the fourth hand is often forced to go to no-trumps, on the theory that his length in the dealer's suit is a stopper. This often gets him into trouble.

Here is a curious deal, to which my attention was called because the hands of dealer's partner and doubler's partner were inadvertently changed, in a duplicate match at some of the tables, with the result that, at some of the tables, the doubler won the game and at some the doubler was defeated.

The dealer bid one heart. By the Robertson rule his hand counts 27, his partner's 3 only, which is 42% of the pack. The doubler has exactly 35%. He holds A K K Q Q J 10, which is just K Q (the equivalent of an ace) above average. His partner holds 2 3%. On the diamond answer to the double the doubler wins the game, by trumping the second heart, getting in with a spade to lead trumps and finesse. Another spade and trump lead and the king falls. Now the two good spades give him two heart discards. Now pull the trump and set up the clubs, with that fourth trump in hand to stop the hearts.

But leave the dealer's and the doubler's hands as they are and transpose the two others. The answer to the double will be a spade and the contract will be set, as it is good for only six tricks.

THE SEPTEMBER PROBLEM

This was the distribution in Problem LXXXVII:

Hearts are tru'mps and Z leads. Y and Z want all seven of these tricks. This is how they get them:

Z starts with the jack of clubs, which A covers and Y trumps. Y leads the ace of diamonds and Z trumps it with the queen of hearts, so that he can lead the heart seven through A. This enables Y to pick up all the adverse trumps, Z discarding the smaller of his two remaining clubs.

A small spade from Y now puts Z into the lead, so that he can make his winning club. The return of the spade gives Y a trick with the jack.

If A refuses to cover the jack of clubs on the first trick, it is obvious that Y can keep his three trumps intact and that Z will come through with a trump at once, after which the ace of diamonds, ace and jack of spades, and the third trump must make tricks.