Sunday, January 21, 2007

Could the Contract Be Defeated? The Software Oracle Knows

When you play in a tournament that gives out deal records, under every board you see the highest contracts that each side can make in the five strains, assuming the play is double-dummy — everyone knows where the cards lie. (This is done using Bill Bailey’s Deep Finesse software.) Competitors in the Flight A/X Pairs last Saturday at the District 3 Winter Regional in Rye Brook, N.Y., were surprised to see that there was a way to defeat three no-trump by South in the diagramed deal. What leads by West work?

The winners of the Flight A/X Pairs, R. Jay Becker of New York and Bob Sartorius of Lake Hiawatha, N.J., played well and had that necessary slice of luck in this deal.

The event had finished. North and South were itching to leave, not having done well. But they had a late play against Becker and Sartorius, who knew they were in contention. (You get a late play when you take so long to complete the first deal of a round that you do not have time for the final board. Playing that deal is postponed until the end of the session.)

South opened one no-trump, showing 12-14 points. Becker (West) overcalled a natural two hearts. North responded with a natural and forcing three clubs. And South converted to three no-trump.

West, assuming South was prepared for a heart lead, tried our well-known sneak attack with the spade six. East played the three under dummy’s jack to show an odd number of spades. (If dummy wins with the ace, king or queen, it is probably best for third hand to signal attitude. But when dummy has only the jack, signaling possession of the ten is surely a waste of time, so giving count is preferable.)

Declarer guessed well, cashing the club ace to drop West’s king. Next, he played a club to his queen. Now, knowing that West had the heart king for his bid, South should have led a heart toward dummy’s queen. Then South would have won nine tricks: two spades, two hearts and five clubs. And if he had done that, Becker and Sartorius would not have won. Jonathan Green of Kingston, N.Y., and Norman Rubin of Monticello, N.Y., would have taken the title.

But declarer led a diamond to the nine on the board. The defenders took advantage of the opportunity. East won with his ten and returned a spade, West taking South’s queen with his king and leading another diamond. East won with his queen and went back to spades, eventually defeating the contract by one trick.

How can the defenders always defeat three no-trump? West must lead a diamond or — yes — the club king. Then the defenders have an answer for anything that declarer tries, taking one spade, one heart and three diamonds.