Contract Bridge

Assume you’re in four spades and West leads the king of clubs, which you ruff. You can’t avoid losing a heart trick, so all your thoughts should be concentrated on not losing three diamond tricks.

You cash the K-A of spades, finding the trumps divided 2-2, and lead a diamond to your king. When this holds, you are faced with the problem of which diamond to play next.

As the cards lie, if you lead a low diamond, you go down one, but if you play the queen — picking up West’s jack and East’s ace on the same trick — you make the contract. In the latter case you will lose only a heart and two diamonds. The play of the queen is thus clearly correct if you could see the East-West cards, but is it possible to justify the queen play if you can’t see the missing cards?

When you consider the pertinent divisions of the missing diamonds after the king wins at trick four, you find that which diamond you play next makes no difference whatsoever if the suit is divided 3-3 or 5-1. In the first case, you always make the contract; in the second case, you don’t.

Only when the diamonds are divided 4-2 does your play make a difference. If you consider all the cases that matter, you find that playing the eight next gains whenever either defender has the doubleton ace, while playing the queen gains whenever either defender has J-x or 10-x.

The cases where one defender is dealt the J-x or 10-x thus outnumber those where one defender is dealt A-x by 2-to-1. The queen play therefore offers a much greater chance of success.