Play bridge according to the odds

Any time declarer sees he can make his contract if a particular suit breaks favorably -- which is a matter of luck -- he should also look further to see whether other means of making the contract are available.

Take this case where South is in four hearts and starts with three sure club losers. The fate of the hand seems to depend on whether he will also lose a diamond trick.

He can draw trumps immediately and then cash his three high diamonds. If the opposing diamonds are divided 3-3, he makes the contract. But if they break 4-2 or worse, he goes down. The prospect of finding the diamonds 3-3 is not enticing, since it occurs in only 36 deals out of 100. South is therefore obliged to seek an alternate line of play that offers a greater chance of success.

Such a method of play is available in this deal, though it is not apparent on the surface. It requires both imagination and some knowledge of probabilities.

When declarer has a combined holding of eight cards in a suit, the outstanding five cards will be divided 3-2 68 percent of the time. South can apply this knowledge to the current deal and can increase his chances of making the hand from 36 percent to 68 percent by playing for a 3-2 trump break.

He wins the spade lead in dummy and trumps a spade with the queen. He then leads a low heart to the nine and ruffs another spade with the king.

Next he crosses to the 10 of hearts and ruffs dummy's last spade with the ace. This exhausts the South hand of trumps, while dummy still has the jack. South has already won six tricks.

The four additional tricks he needs are obtained by crossing to dummy with a diamond, drawing the last opposing trump and then cashing two more diamonds. As it turns out, the diamonds are divided 4-2, but South nevertheless has 10 tricks to show for his efforts.

(c) 2007 King Features Synd., Inc.