Do you try to split or to finesse?

David Mamet said, “A stage play is basically a form of uber-schizophrenia. You split yourself into two minds — one being the protagonist and the other being the antagonist. The playwright also splits himself into two other minds: the mind of the writer and the mind of the audience.”

Occasionally at the bridge table, you will be of a split mind when trying to decide between two possible lines of play. In this deal, for example, South is in four spades. West leads a low heart. East wins with his king and shifts to a trump. What are declarer’s two reasonable lines of play, and which is the better?

South was tempted to raise one notrump to three no-trump, which would have worked fine if East had led fourthhighest from his longest and strongest, but less well if East had chosen the heart ace as his opening salvo.

South started with nine top tricks: six spades, one diamond and two clubs. If East had not shifted to a trump, declarer could have taken a heart ruff on the board. Now that was impossible.

The original South drew trumps, played a club to the ace and returned a club to his jack. However, the finesse lost, and West led another heart, giving the defenders three hearts and one club.

The finesse was, in theory, 50-50. But there was a better plan, relying on a 3-2 club break, which had an a priori probability of 67.8 percent.

At trick three, South should have led a low club from his hand and played low from the board. That would have brought down the curtain on the defense.