HINTS ON AUCTION BRIDGE

Sun (Auckland), Volume III, Issue 774, 21 September 1929, Page 34

HINTS ON AUCTION BRIDGE

Supporting The Partner's Bid (Written for THE SUN by "Caliban."—Copyright in New Zealand.) I NOTICE that many of those who play Auction regularly have never ■worked out for themselves, or even attempted to work out, the principles upon which they should support their partners’ bids. They are content to rely upon an instinctive judgment of the situation. Where a player has an exceptionally keen “card sense” this is, perhaps, as good as anything else; native ability, combined with experience, will ensure the right decision, though the maker of it may not be able to offer a reasoned explanation. But such combination of native ability and experience is not bv anv means common; and the average player, “muddling along” in what w"e call our ‘‘characteristically British” fashion, throws away hundreds of points every week —merely because he is too lazy to apply his mind systematically to an ever-recurrent aspect of the game. Let us attempt, then, to analyse this problem of the supporting bid. It involves, as a moment’s consideration will show, two related questions: — (1) How many tricks must one’s hand be worth to enable one to support one’s partner? (2) How can the trick-value of the hand be calculated? We will deal with the two questions separately. Minimum trick-values for a supporting bid. The mathematics of the problem are extremely simple, yet I doubt whether one player in ten attempts to work them out. Some examples will make them clear. Suppose, first, that at the score of Love-all, Z, the dealer, has opened the bidding with One Heart. Suppose that A, on his left, has over-called with One Spade. It is now Y’s turn to bid. How many probable tricks must he hold in his hand to support his partner s call? The facts available are these:— (1) Z has called One Heart. He therefore expects (in the mathematical sense) to make at least seven tricks if frhe hand is played in Hearts. (2) As far as appears from the two calls so far made, there is nothing abnormal abrmt the distribution of the cards. Now for the inferences from these facts: (1) Z expects to make seven tricks if Hearts are trumps. (2) He is entitled to assume that the tricks he cannot make himself will be equally divided between the other three players. (3) He estimates, therefore, that his own hand, if played in Hearts, i* worth four tricks at least, and he may be counting on Y for as many as three. This last statement is perhaps not self-evident. The shortest method of demonsitrating that it represents Z’s expectation is a very simple a'gebraical formula: Bet x be the trick-value of Z’s hand if played in Hearts, 13 x Then x plus = 7 i.e., x = 4. 3 f>r, put into words: there are thirteen tricks in all; Zis hoping, with Y’s assistance, to make seven; he is entitled to assume that Y will make oneihird of the tricks that he does not make himself; and the minimum strength in his own hand that satisfies these conditions is four tricks. We now know exactly where Y stands. If, with Hearts trumps, his hand is worth more than three tricks, it is his duty to support his partner unless, of course, he has game in some other call). If his hand is worth less than three tricks, he should pass. The same process of reasoning is applicable, whatever Z'b initial call. Suppose that he has opened with Three Hearts, and that A has called Three Spades. Then, applying the same formula as before to arrive at Z’a estimate of the value of his hand, we get 13 x x plus = 8 3 where x is the minimum trick-value of Z’s hand. Whence, x = 7. In this case, therefore, Z is only “expecting’’ two tricks from Y, and the latter should “lift” the call if he assesses the value of hi-a hand at more than two. To conclude this part of the argument, a table may be drawn up showing the minimum (in tricks) that Y’s hand should be worth to enable him to support his partner’s call:—

This table must not, of course, be too rigidly interpreted. Special considerations—*.g., the psychology of the players, their known tendency to under-bid or ever-bid, the state of the score, and the intervention of a pre-emptive bid —must all be taken into account. Next week I will deal with the second part of the question; the calculation ot the trick-value of the hand.

"Where declarer's (Z's) initial bid is He is entitled to assume that liis partner's hand is worth And his partner (Y) should not raise him unless his hand is worth One 3 tricks 3^ —4 tricks Two 21 3 —34 „ Three 2 Four j* „ 2 —24 „ Five i 34—2 Six i >, l —14 „