Bridge

Dear Mr. Wolff: You recently wrote that the chance of a suit splitting 4-3 was 60 percent. Since there are seven different lengths each opponent could have, why isn’t the chance closer to one in three? – Can of Worms, Elmira, N.Y.

Answer: When an odd number of cards are missing, the chance that they split as close to evenly as possible is approximately two-thirds, the odds going down as the total number of cards involved increases. When an even number of cards are missing, the chance that they split exactly evenly is one third, the odds going down as more cards are involved.

Dear Mr. Wolff: I held ♠ Q-7-3, ♥ Q-10-9-6-2, ♦ A-7-5-2, ♣ K. My partner opened one club and the next hand bid three diamonds. What should I do now? – Stepping Up, Tulsa, Ariz.

Answer: I’d bid three hearts and hope to get raised, or to hear three spades so that I could bid three no-trump. You are not worth committing the hand to game, but what else can you do? Anything else is too extreme.

Dear Mr. Wolff: Are there any guidelines about discarding honors such as kings or queens in midhand? – Riches to Burn, Houston

Answer: If I understand you correctly, you want to know whether the discard of an honor denies a higher card in the suit. I think so. For example, if I had to discard from A-J-10-9, I’d pitch the 10 or nine. The jack tends to deny a bigger card. Likewise, the king suggests solidity down from the king, but not the ace above it.

Dear Mr. Wolff: With ♠ A-Q-7-3-2, ♥ 4, ♦ Q-10-8-2, ♣ A-J-3, what would you call if you heard one heart on your left and four hearts on your right? I can see how passing, doubling, and bidding four spades might all work. – Hot Seat, Doylestown, Pa.

Answer: You are absolutely right, and my vote goes for the bold (or foolhardy) bid of four spades. The real reason for acting is that the jump to four hearts is very wide-ranging. Even when LHO might double me for penalties, he will not know if his partner has only shape, or some high cards, too. They made you guess, so return the favor.

Dear Mr. Wolff: Since it is year-end now, can you summarize what happened to you in bridge in 2007 – and went on in the world at large? – Curious George, Lakeland, Fla.

Answer: On a personal note, I was delighted to qualify to play in the Bermuda Bowl in Shanghai in the seniors division. At the world level, the thing that most distresses me is the shift of focus away from juniors. If we (the world and the Americans) don’t spend money on juniors, the game will die. Schools in Europe (especially Poland) and in Israel have introduced bridge successfully. Why can’t we?