Two pots boiling on the range

Even though you don’t need to be a mathematician to play good bridge, it helps to know some percentages. When there are two lines of play available, it is useful to be able to calculate the approximate probabilities of success in order to decide which is better.

In today’s deal, South was in three no-trump after a straightforward Stayman sequence. West led the spade king and had no intention of switching suits. What should declarer have done?

South saw that he had eight top tricks, instant winners: one spade, two hearts, two diamonds and three clubs. From where would the extra trick come?

Clearly, the heart suit could have produced a third winner, but if South had to lose a trick in the process, the defenders would surely have cashed a fatal number of spades. Declarer had to get the ninth trick without losing the lead.

If either opponent had the singleton heart queen, or if the heart finesse worked, that would generate a third heart winner. Chance of success: a little over 50%.

The other possibility was a 3-3 club break: a 35.53% shot.

That suggested taking the heart finesse. However, on this deal it was possible for declarer to try both suits. After winning trick one or two with the spade ace, he led a heart to his ace and cashed his three top clubs, ending on the board. As the suit did break 3-3, South crossed to hand in a red suit and cashed the club seven for his contract. If the clubs had not split favorably, declarer would have taken the heart finesse.

Combine your chances whenever you can.