Contract Bridge

Dear Mr. Becker: We had a big argument about this hand where South was declarer in four spades and West led a heart. South won with dummy’s ace, played a spade to the ace and then led a low spade, losing to West’s king. South later lost the jack of spades to the queen and a diamond trick, but he wound up making four spades.

The argument was over whether South played the spades correctly or whether he was just lucky. Shouldn’t he have finessed the ten of spades at trick two? I know he would have gone down if he had done this in the actual deal, but wouldn’t that be the winning play in the long run? Sincerely yours, Constant Reader.

Well, the answer is that South was correct in the way he played the spades, not only because he succeeded, but because his approach was in accordance with the percentages.

Problems like this are susceptible to fairly simple computation. Since declarer’s sole aim is to avoid the loss of more than two trump tricks, if possible, he starts out by ignoring all the spade combinations where the play of the ten or the ace is immaterial. These would include those hands where the trumps are divided 6- 0, 5-1, or 3- 3.

The only really pertinent hands are those where the spades are divided 4-2, with West holding the doubleton. West’s doubleton can consist of K- 9, K- 8, K-7, K- 6, Q- 9,

Q- 8, Q-7, Q- 6 (in which case the ace play is better than the ten), or it can consist of 9- 8, 9-7, 9- 6, 8-7, 8- 6, 7- 6 (in which case the ten play is better than the ace). The only other case, where West has the K- Q alone, does not matter because either play makes the contract.

As there are eight cases where playing the ace wins, and only six where playing the ten wins, it is better to play the ace and a low spade.