HINTS ON AUCTION BRIDGE

Sun (Auckland), Volume III, Issue 822, 16 November 1929, Page 27

HINTS ON AUCTION BRIDGE

A Non-Free Double lIT W? ra * -Caiitan."— Copyright in .N em Z"alaji4 ) H- go. the or ~ra.» Love-ail >» t ® rubber game. Z. the dealer, opened the bidding with One Spade. A, on his left, hell the following curds; gpadet K ‘ Hearts AK x x Diamonds A Q Clubs *x x u j c aU« One % So Bi. : B, Two Clubs; Z. Two Spades; A. Two No-Trumps; Y, No Bid; B, No Bid; Z, ■piiree Spades n hrreupou A not uunaturally doubled. To bis eon 'emotion, the distribution 'of the cards proved to be as i ■—T

TV- .p s b• ‘ '*»f r u:»l plu> ing of the card- ttb* (a* the reader will iff, that Z rr. i it ' •• |i, ' p art ;■*»*•! the void > He made two trump?, rh« I ruffcii twice punimv and Hearts three times in hn own hand. N 1 B that i ant, in P,,, ; 4 ffii-|e to draw attention. “Bad link, partner, wasn’t it?-’* said A. p. “ » l.i 1 ki n dc«■ ■i. But it wasn’t a free double, you know. - ’ A: • Surelv, w ith a ha- ! like none, that « onsideration hardly enters into it. nr ou I*. I •on . off. B: 4 4 All the aamr, I think '"in double v\ n - v\rmr,. To double your opponents out is the one unpardonable t.fl>»n-e.' Now l think that B w avuong. and that his diettim (to which, 1 am Hwar> . many g<>od pla\n-. sol..- '-ibe , i - quite untenable. It is true, as B pointed out to A. that the lattei ’s unfortunate double cost them 27 d- ~r 250 -= .127 points, “and ••ill’’ (as B said) ‘‘for the sake of a possible But B, like jo n any pla; ers, was 1 >oking no farther than Ins nose. What he saw was the .'■27 which A’s double ‘‘threw away”; what be tailed to see was that A’s expectation, when he doubled, was a substantial balance of points in his favour. And since that was the ease, it would have been wrong of A not to double. la Hi w - summarising the position, 1 am using the term “expectation” in its mathematical sense: i e., it has reference, not to what A 44 hoped’* n> get, but to what be w ould be certain to got, on the average, if be made the same call in the same circumstances a sufficient number of times. And this is the onb criterion by which the rightness or wrongness of his calling ran properly be judged. I should add that, in saying that A’s cxpceta‘ : on when he doubled was ‘• a substantial balance of points in his favour,” I am making a statement that Xam not prepared to prove. The problem, as a problem in mathematics. is too complicated to be work*- l out. But the following demonstration ot' the reasonableness of mv statement will, I think, carry conviction. Let us* put ourselves in A’s place. Given his hand, and the calling — winch are all the data in liis possession—it seems reasonable to assume that, for every chonc® Z has of making his contract, there are, say, ten chances of his going down one trick, five chances of his going down two trick?, three chances of his going down three tricks, and one chance of his going 4own four tricks. i These assumptions are purely arbitrary, but T think Ihcv »re on the safe -dde. > We .on then calculate his expectation as follows:(i) If Z call is not doubled:—* Out of twenty hands, he will— Win 27 points on one occasion. l.ose 50 points on ten occasions. Lose 300 points on five occasions. Lose 150 points on three occasions. w Lose 200 points on one occasion. ,\ hi* expectation is: 27 2b 20 Hr a loss of $1 points. (ii) If Z*s call is doubled: Out of twenty hands, he w ill— Win 551 points on one occa ion. Lose 100 points on ten occasions. Lose 200 points on five occasions. Lose 500 point? on three occasions. Lose 400 points on one occasion, his expectation is: 354 20 20 f>r a loss of 147 points. And A s double, given the arbitrary assumptions which underlie ‘Uiese calculaWins, stands to win 66 points (147 - s>l) for his side. He would therefore be guilty of an “unpardonable offence,’.’ not in doubling, but in failing to double.' for the one certain method of losing at Bridge is habitually to defy—as many players do—the a priori odds. ■a. a* m ■ mm mmm m mm