ACES ON BRIDGE

The second qualifying session of the Kaplan Blue Ribbon Pairs from San Diego last fall threw up a challenge for the analysts. Debbie Rosenberg posed this problem: What is the optimal contract for North-South on best play and defense? With the heart finesse working, you can make six no-trump by setting up a club or building a second spade trick, should the opponents lead that suit. But how about seven diamonds, reached after Blackwood and an ask for the trump queen? The line of play you could follow in six diamonds as North on a trump lead (win the diamond king, cash the club ace and club queen, play a diamond to dummy, take a club ruff high, then draw trumps and eventually take the heart finesse) seems to work. Ah, but what about an initial heart lead? Your late entry to the heart suit has now gone. But Deep Finesse (the analytical tool that looks at best play by all four hands) still obstinately insists that seven diamonds can be made. Back to the drawing board! The solution is not intrinsically complex, but the choice of lines makes it hard to spot. Win the heart jack, ruff a heart, then draw four rounds of trumps to reduce down to a seven-card ending. East is caught in a three-suit squeeze on the last trump. To reduce to fewer than three hearts and four clubs would immediately be fatal. But to retain those cards, East must pitch the spade king. Declarer can unblock clubs, cash the heart ace and king, then finesse in spades.

I have hardly ever known a mathematician who was capable of reasoning.

— Plato