Contract Bridge

More than just a guess

Opening lead — queen of clubs. Consider this deal where South is in four hearts and must make a critical guess to make his contract. Let’s say he wins the club lead with the ace, plays the A-K-Q of trumps, discarding two diamonds from dummy, leads a club to the king and ruffs a club. Declarer now plays a spade to dummy’s jack. East takes the king and returns a diamond. West wins with the jack and continues with the ace. South ruffs and leads another spade. When West follows low, declarer must guess whether to play the queen or the nine from dummy. If he thinks West has the ten, South should play the nine; if he thinks West has the ace, South should play the queen. Many players may think that the card declarer should play from dummy in this situation is an out-andout guess. This is not correct, however. Without going into the mathematical details of why the right play is the queen, the fact is that in those cases where declarer’s play matters — and assuming there are no clues to indicate otherwise — the queen play will be successful approximately twice as often as the nine play. These odds presuppose that West, who knows from the earlier plays that declarer started with three spades, is a first-rate defender who would not go up with the ace if he originally held A-x-x, A-x-x-x or A-x-x-x-x of spades. He would follow low to give declarer a chance to go wrong. He would also follow low each time if his spades were headed by the king instead of the ace. The only pertinent cases are therefore those where East holds the ace and ten, the king and ten or the ace and king of spades. The first two cases together occur twice as often as the last case, and that is why the odds are 2-to-1 in favor of playing the queen on the second round of the suit.