Which finesses should South take?

Rex Stout, who wrote the Nero Wolfe novels, said, “To read of a detective’s daring finesse or ingenious stratagem is a rare joy.”

In today’s deal from Steve Conrad of Manhasset, New York, South is in three no-trump, faced with finesses in three suits. What is his optimum strategy?

This is the most common auction of all, leading to the most popular contract. But what is the least common contract?

South starts with five top tricks: one spade, two hearts, one diamond and one club. If both black-suit finesses are working, that would get his winner total up to nine. Or if both diamond honors are onside, that would also be good enough. But if a finesse loses, the defenders will presumably establish West’s heart suit. Then, if West can regain the lead, he might cash too many tricks for declarer.

That suggests starting with the spade finesse, because the spade king is West’s only possible entry. But getting to the dummy for that finesse introduces other complications.

Much simpler is to take two diamond finesses. The first loses to East’s jack and a heart comes back, but South ducks that, wins the next heart, then — key play — runs the club queen. (Agreed, if declarer deduces who has which kings, this isn’t necessary, but it avoids guesswork.) East takes that trick and shifts to a spade, but declarer wins with his ace, repeats the diamond finesse, and has nine tricks from one spade, two hearts, four diamonds and two clubs.

The least common contract is five no-trump, which has all of the risk for no gain.