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Combine Your Chances

  by Richard Pavlicek

You don’t have to be a mathematician to be an excellent bridge player. In fact, it has been evidenced over the years that mathematical theorists seldom reach the top echelon in bridge. Why not? Because it is rarely necessary to know the exact odds or percentages to play a bridge hand correctly. As the story goes, a good mathematician can quote you his exact chances of success — probably to at least two decimal places — after he has gone down in his contract.

The key to successful play is to have a logical and practical mind. Try to find two or more chances, then look for a line of play that will take advantage of as many of the chances as possible. Witness this deal from a recent Swiss team event:

North dealsS K 9 4 2WestNorthEastSouth
None vulH A 21 DPass1 NT
D A Q 8 6 4Pass2 NTPass3 NT
C A 4PassPassPass
S A 7TableS Q J 10 8
H K 10 7 6 5H J 9 8 4
D 10 7D K J 9
C 8 6 5 2C 9 7
S 6 5 3
H Q 3
D 5 3 2
3 NT SouthC K Q J 10 3

You breathe a sigh of relief when you win the H Q at trick one. There are eight top tricks: two hearts, one diamond and five clubs. Pretend you can’t see the E-W hands and ask yourself how you would play. Would you (1) run the clubs, (2) lead a diamond to the queen, or (3) lead a spade to the king?

First, you cannot gain a trick in clubs; you already have five. So options 2 and 3 are the only chances to make your contract. It is very important which chance you try first.

If you take the diamond finesse and it loses, a heart back will knock out your last stopper. Now you are history! The opponents can set you regardless of what you do next.

The right play is to lead a spade to the king. This wins as the cards lie. But note that if East were able to capture the S K, you would still be alive to try the diamond finesse (except in the extreme unlikelihood that East has S A-Q-J-10-x). Leading the spade first gives you two chances instead of just one.

Article 7H57   MainTop   Combine Your Chances

© 1996 Richard Pavlicek