The second-degree assumption is key

Eric Temple Bell, who was a Scottish-American mathematician and science-fiction writer, said, “Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.”

At the bridge table, you sometimes make an assumption about the location of a specific card. When you do, though, ask yourself if that assumption might also permit you to draw a conclusion about another card — what is known as a second-degree assumption.

How does that apply to this deal? South was in an ambitious fourspade contract. West led the heart ace, cashed the heart king and continued with a third heart. What assumptions should declarer have drawn, and how would they have affected his line of play?

The North hand had nine losers (two spades, three hearts, two diamonds and two clubs). That is the normal number for a single raise, but North had 10 points and four trumps. Then South, who had seven losers (two spades, two hearts, one diamond and two clubs), should have passed. But he succumbed to the lure of a vulnerable game bonus.

The original declarer played a spade to the king at trick four, so went down, losing two spades and two hearts. South should have assumed that West held the club king, giving him 10 known points. That made it slightly more likely that East had the spade ace. West, with that ace, might have entered the auction over one spade, or at least thought about it for a few moments.

If declarer had played a diamond to the queen and continued with a low spade from the board, the contract would have made.