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Logic Defies Mathematical Odds

by Richard Pavlicek

Today’s deal, from a recent practice match, illustrates the use of bridge logic to choose the correct play. See if you can determine declarer’s rationale for making the winning guess. All four players were experts.

 4 SouthBoth Vul A J 10 8 6 2 K 9 6 3 A 3 2 WestPass NorthPass EastPass SOUTH4 9 7 2 10 3 A J 10 7 K Q J 5 K Q 5 A 6 Q 8 2 10 9 8 7 6 Lead: K 4 3 K Q J 9 8 7 5 4 5 4 4

The opening bid illustrates the “rule of two, three or four,” a modern preemptive strategy to overbid two tricks at unfavorable vulnerability; three tricks at equal vulnerability; or four tricks at favorable. South can win seven tricks on his own, so with both sides vulnerable (equal) he contracted for 10 by opening four hearts. This was passed out.

West led the club king, won by the ace, and declarer led a heart to his king as East ducked. The heart queen was led to East’s ace (declarer threw a spade from dummy), and East returned a club which South ruffed. A spade was led to the jack and queen, then another club was returned and ruffed.

Declarer cashed two more trumps to no avail then faced the crucial decision: Should he take a second spade finesse, hoping that West has the king? Or should he lead a diamond, hoping that West has the ace? The former is correct by mathematical percentages; but declarer defied the odds. He won the spade ace (in case the king fell), ruffed a spade and led a diamond to make four hearts. Was this a lucky guess?

Declarer did some logical thinking: What situation am I playing for? What could the defense have done about it? If West held the spade king, he could have foiled declarer’s opportunity in spades by playing the king on the first round — a play that a good player would find. (This would prevent declarer from winning more than one spade trick because dummy held no outside entry.) Why didn’t West do this? Evidently, because he doesn’t have the spade king. Therefore, the only remaining chance is that West has the diamond ace.

Winning tip: A knowledge of mathematics may be helpful, but it is no match for logical deduction.

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