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# Counting the Hand Beats All Odds

by Richard Pavlicek

Today’s deal was submitted by a reader who, as South, became declarer in three notrump after the bidding shown. West led the heart queen, East overtook with the king (a standard unblocking play), and declarer held up the ace until the third round on which East discarded a club.

 3 NT SouthE-W Vul A 10 3 9 7 5 A Q 10 3 K 6 4 WestPassPass NORTH1 3 NT EastPassPass South2 NTPass 8 5 Q J 10 8 2 J 8 6 5 Q 10 Q J 9 6 4 K 4 4 J 9 7 5 3 Lead: Q K 7 2 A 6 3 K 9 7 2 A 8 2

The problem, of course, was how to play the diamond suit. Declarer reasoned that East was more likely to have length in diamonds because of his shortness in hearts, so he began by winning the ace and queen. Curtains! East showed out and now there was no way to finesse West for the jack. The reader asks, “Was my reasoning correct?”

Yes, at this juncture. When one suit is known to divide in lopsided fashion (as hearts here), the odds favor a compensating division in another suit. One would expect East to be longer in diamonds — most of the time. I emphasize the latter because it is based on probability, and as any racetrack bettor knows, the favorite doesn’t always win.

The reader committed himself too soon. He should have sought further information about the enemy distribution before tackling the diamond suit, or in bridge parlance: Try to get a count of the hand. After winning the heart ace, the best maneuver is to lead a spade toward dummy and finesse the 10. (This is safe because East is out of hearts.) Assume that East wins and returns a spade.

Declarer then cashes his top cards in spades and clubs to learn that East began with five spades (affirmed when West shows out on the third round), two hearts and at least three clubs (remember, East discarded a club on the third heart). Therefore, it is impossible for East to hold four diamonds. Declarer now has a certainty by winning the diamond ace followed by the king. Either the suit will divide three-two (in which case the jack must drop) or, as in the diagram, East will show out to reveal the finesse against West.

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