Contract Bridge

Before a declarer concludes he can make his contract only if a particular suit breaks favorably -- which is a matter of luck -- he should look further to see whether some other means of succeeding is 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 top 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 that will occur 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 easy to spot. 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 present deal and can increase his chance of success 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 trump to the nine and ruffs another spade with the king.

Next he crosses to the ten of hearts and ruffs dummy’s last spade with the ace, bringing his total thus far to six tricks. The South hand has no more trumps, while dummy still has the jack.

The four additional tricks

he needs are obtained by crossing to dummy with a diamond, drawing the last opposing trump -- on which declarer discards a diamond -- 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.

Tomorrow: The magic of card-reading.