Playing the odds

One reason bridge is compelling is that it has diverse elements such as mathematics and psychology. Those two may complement each other — or conflict.

Two players asked me how South should play at today’s 3NT when West leads the deuce of spades. At the table, South captured East’s jack, took his ace of hearts, led a club to dummy and returned a heart to finesse with his jack.

West produced the queen and led the queen of spades, and South won and took the king of hearts: A 3- 3 break would have given him a ninth trick. After East discarded a spade, South still had a chance, but when clubs broke 4- 1, he wound up going down.

“I think it’s correct to lead a club at the third trick and play low from dummy,” one player observed. “If clubs break 3- 2 or 4- 1, declarer wins four clubs, two spades, two hearts and a diamond. We’ve tried to compare the two lines of play percentage- wise, and it looks like a toss- up.”

Attacking the clubs at the third trick is superior. Cold numbers aside, if declarer led a low club at the second trick and West followed, declarer could confidently play low from dummy, expecting the suit to break decently: If West had started with J- 10- 9- 8- 2, his opening lead would have been the jack of clubs.

It appears that South does best to take the king of clubs at Trick Three. If East- West follow, South ducks a club next and is sure of nine tricks. If East has all five missing clubs, South leads a club to dummy and a heart to his jack. If the finesse loses, he can still hope for a 3- 3 heart break.