Some bridge players, when faced with a guess or two, rely on their card reading or human frailty. Others prefer to stick to mathematics.

In today’s deal, South pushed into seven hearts. After West led a trump, and East discarded a diamond, how should declarer have planned the play?

North’s two-no-trump response was the Jacoby Forcing Raise, promising four or more hearts and at least game-going values. South twice used Roman Key Card Blackwood to learn that his partner had one key card (the diamond ace), the heart queen and the club king – nice!

South seems to have to find the club queen, since he can ruff his two low spades in the dummy and dummy’s diamond seven in his hand. So the original declarer drew trumps ending in his hand, then led the club jack. He assumed that if West had the club queen, he would cover or would think about it. However, when West played low smoothly, South won with dummy’s king and returned a club to his 10 … and went down one. Welldefended, West.

The mathematician sees that he can also get home with four spades, five hearts, one diamond, two clubs and a club ruff in the dummy after discarding two clubs on the third and fourth spade winners. When there are two suits missing the queen, the best play is to cash the ace and king in the suit with the greater number of cards (here, clubs), and if the queen does not fall, to finesse in the other suit (spades). Since West had a doubleton club queen, that would have worked.