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# Look at the Forest, Not Just a Tree

by Richard Pavlicek

Today’s deal, from one of my advanced lessons, provides some insight for the aspiring player. South becomes declarer in six spades after a Blackwood auction. Note that North’s five-club bid showed zero or four aces; South, of course, knew which.

 North deals A 6 5 2 West North East South None vul A K 7 2 1 Pass 1 A 3 Pass 4 Pass 4 NT A 9 4 Pass 5 Pass 6 Q J 8 7 Pass Pass Pass Q J 10 5 9 6 10 5 2 J 9 8 7 6 J 6 5 3 Q 10 8 7 K 10 9 4 3 8 4 3 K Q 4 6 South K 2

West leads the heart queen, taken in dummy, and the spade ace is cashed on which West drops the jack. Should declarer now play to drop the queen or should he take the finesse? Let’s see how this problem might be solved by three players of different skill.

Average Ann recalls the maxim, “eight ever; nine never,” which dictates to finesse for a queen with eight cards or fewer. Therefore, she continues with a spade to the king… easy hand.

Serious Sam knows the principle of “restricted choice,” which states that an opponent who drops one of two equal cards is less likely to hold the other. Therefore, he leads a spade to the ten. Oops, down one.

Sam made the correct percentage play in the spade suit. West was dealt one of two spade holdings: jack singleton (6.2 percent chance) or queen-jack doubleton (6.8 percent), but in the latter case West has a choice of plays. Assuming that West plays without bias, the probability of the jack from queen-jack would be only 3.4 percent (half of 6.8). This makes the singleton jack more likely.

Expert Elaine (male chauvinists take note) knows all about restricted choice, and she would play as Sam did if her contract depended on the spade suit. But she is not blinded by a single tree in the forest and notices a second chance. Therefore, she leads a spade to the king. Sweet!

If the spade queen did not fall, Elaine’s backup plan was to cash both top clubs, three top diamonds (throwing a club from dummy) and the remaining top heart; then a spade is led to East, who must yield a ruff and discard (unless he held another heart).

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