Is the Principle of Symmetry Valid?

Today’s deal was played by Vernon Pope of Boca Raton, an octogenarian with more spunk and vigor than most people half his age. One can only marvel at his activity calendar, jammed with bridge, travel, theater, movies, concerts — you name it.

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

Pope, South, opened one club and then rebid one spade after his partner’s diamond response. Technically, he should rebid one heart (up-the-line), but that is a trivial matter; he liked his spades better. North jumped to three diamonds, South bid three notrump to show his heart stopper, and North jumped to five clubs.

Pope reasoned that North would have freakish distribution with good clubs; and, since he held extra high-card strength with control (ace or king) in every suit, he continued to slam. This was fine judgment; an expert couldn’t have bid any better.

West led the heart ace and continued the suit. (This lead made no difference as one of dummy’s hearts could have been discarded on the spade ace.) Declarer had to guess how to play the trump suit to make his contract.

The normal play with nine cards missing the queen is not to finesse, a la “eight ever, nine never,” but the advantage is slight (about 12 to 11). Good players look for other clues. Declarer noted that his own hand had a singleton, and dummy held a void; so it seemed logical that one of the opponents would also hold a singleton or void. Therefore, after cashing the club king, he tried the finesse. Ouch! Better luck next time.

Was declarer’s logic valid? It certainly sounds convincing, but the answer may surprise you. The so-called “principle of symmetry” is bunk. The probabilities of the division of enemy cards are not affected by the way cards are divided between declarer and dummy. The only significant information is what declarer knows about the enemy hands. On this deal the only clue is that neither opponent bid, which suggests an even club break. (With a singleton club, an opponent would be more likely to bid.) Therefore, the odds of dropping the queen are actually slightly better than 12 to 11.

Column 7D26 Main

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© 1989 Richard Pavlicek