Puzzle 7F59 (Jul 99) by Richard Pavlicek

Optimum Contract

In bridge articles one occasionally comes across the phrase “optimum contract,” which refers to the highest scoring contract a side can make on a particular deal against best defense. Note that in some cases this contract must be declared from a specific direction to prevent a damaging opening lead. Consider the following deal:

9
J 10 9
A Q 4 3 2
A K Q 2
—
—
J 10 9 8 7 6 5
8 7 6 5 4 3 [W - E] A K Q 8
A K Q 8 7
K
J 10 9
J 10 7 6 5 4 3 2
6 5 4 3 2
—
—

A. What is the optimum contract for North-South?

B. What is the optimum contract for East-West?

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Solution

A. The optimum contract for North-South is three spades, played by South. Note that West has no hearts, so whatever he leads is won in dummy and declarer gets four discards as East follows suit. Then the

Q is led and if East ruffs low, South can either discard his last heart or overruff and win nine tricks. (East must not ruff high, else South wins 10 tricks.)

B. The optimum contract for East-West is less obvious. It is easy to see that East (or West for that matter) can make two notrump — East has eight winners and North has five, so the play is straightforward. But can they do better? Can East make three hearts? No, only the same eight tricks are available.

What about in diamonds? Only eight tricks are available by West, although East can make three diamonds — four of West’s clubs go away because South must lead a major suit. Alas, making three diamonds is still an inferior score to two notrump, so we’re back to square one.

Enter the bizarre. The optimum contract for East-West is also three spades, played by East. Regardless of the lead, East wins one top trump and five hearts. Note that South must now ruff all plain-suit leads and repeatedly lead trumps, allowing East to score the eight spot as his ninth trick.

As Victor Mollo’s Hideous Hog would describe it, “Curious hand; makes three spades both ways.”

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	9 J 10 9 A Q 4 3 2 A K Q 2
— — J 10 9 8 7 6 5 8 7 6 5 4 3		A K Q 8 A K Q 8 7 K J 10 9
	J 10 7 6 5 4 3 2 6 5 4 3 2 — —