ACES ON BRIDGE

What is best in mathematics deserves not merely to be learned as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement. — Bertrand Russell

This deal comes from the fertile pen of Steve Bloom, who showed me a deal where he had missed a subtle point in the ending by being too thrifty with his resources.

Declaring two spades after having blown your opponents out of the auction, you get a top club lead and continuation as East echoes. (Yes, a trump shift was necessary by West.) You ruff the second top club, play a diamond to the king and duck a diamond to East’s ace.

Back comes a heart, and you win with the queen as West encourages. Now you play a third diamond to West’s queen, East pitching a club, and West leads a second heart to East’s ace. You win the third round of hearts in hand as West follows with the jack. Next, you ruff the club jack in dummy as West produces the queen, persuading you that East has the spade king; otherwise, West would have acted over your no-trump opener. When you lead dummy’s diamond, you are ready to overruff East and play the ace and another spade. But what if East discards his last heart? You must ruff your winner anyway, and then you can lead your fourth club. West will follow, and East will be endplayed to lead away from the spade king when he overruffs dummy. So why must you ruff your winner? If you do not, pitching your club on the diamond jack, you will have to guess whether to lead a spade to your seven or to the 10 in the three-card ending. ANSWER: The raise to two hearts can be based on either four trumps or an unbalanced hand with three trumps, so many people use two no-trump here as a forcing relay to find out partner’s shape and range. I think a simpler route is to bid three no-trump and let partner decide which game he wants to play. If you would like to contact Bobby Wolff, email him at