Contract Bridge

When all is said and done, bridge is essentially a game of percentages.

You make a bid because you think it will work out best in the long run; you make a particular play because you think it’s the one most likely to succeed. It’s really just that simple.

Consider today’s deal, for example. South reaches six notrump, and West leads a diamond. Declarer can count 10 sure tricks -- two spades, two hearts, four diamonds and two clubs -leaving him two tricks short of his mark.

South can see two different sources for the extra tricks he needs. One is in clubs, where he has a finesse available. If East has the queen, the lead of the jack from dummy, followed by a second club to the ten if the jack is not covered, will do the job very nicely. The alternative lies in hearts, where declarer appears to need a 3-3 division of the opposing hearts.

If this is as far as South goes

in his thinking, he might very well choose the club finesse, since most players have learned that a simple finesse is a 50 percent proposition, while a 3-3 break is not nearly as likely (36 percent).

This would be a gross oversimplification of South’s actual chances, however, because it does not take into account another lie of the opposing hearts that would be beneficial -- namely, that either opponent might have been dealt the Q-x or J-x of hearts. In that case, the play of the K-A would drop one of the missing honors, allowing declarer to establish four heart tricks by conceding the ten to the missing honor.

This possibility, when added to the chance of a 3-3 break, would give South a total chance of 61 percent to make the slam -- significantly better than that offered by the club finesse. (If an honor does not fall when the top hearts are cashed, declarer’s best percentage chance would be to continue with a third round of hearts.)

In the actual deal, the recommended approach solves declarer’s problem very quickly, while the contract would have virtually no play after the club finesse loses.