Can you explain to me how to calculate the odds for a 2-2 split and a 3-1 split when missing four cards in a suit? How does this calculation apply to playing for the drop of a missing queen?

Crunching the Numbers, Hamilton, Ontario

When missing four cards to a queen, after, say, cashing the ace and leading toward the king, the chances of a 2-2 break are in abstract slightly better than 50 percent. One hand has 12 vacant slots for that queen, and one has 11. However, it is worth emphasizing that the slightest clue, such as that one hand has five spades and the other has three, can shift the odds significantly.

Playing Pairs, at favorable vulnerability, if you pick up ♠ —, ♥ 6-4-2, ♦ A-K-8-6-5-4-3-2, ♣ 9-7, is your hand worth (or nearly worth) an opening bid, or would you go for a pre-empt? If the latter, at what level?

Wild Thing, Honolulu, Hawaii

I would never consider a one-level opener here. The choice is between a four and five-level pre-empt, and I could go either way. A three-level pre-empt lets the opponents in cheaply and also doesn’t do justice to these offensive values, even if it does leaves three no-trump open for our side.

I held ♠ Q-8-2, ♥ K-10-6-4-2, ♦ Q-3-2, ♦ Q-7. My partner opened one diamond, and the next hand bid two clubs. I thought my choice was to raise diamonds or double, since bidding two hearts seemed too aggressive. What was the best course of action here?

Time after Time, Salinas, Calif.

Passing is far from absurd; your partner will reopen with club shortness. If your partner has club length and a minimum hand, maybe you should stay out. Incidentally, a negative double with just spades might work better than with hearts, since you can correct a minimum response so much more efficiently. I don’t like a raise to two diamonds here; your trump support simply isn’t good enough.

The new ACBL regulations for opening and overcalling one no-trump state that you can make that call with a singleton ace, king or queen. Should we alert if we use this new style? If the answer is yes, then for how long does this apply?

One-Armed Bandit, Tampa Bay, Fla.

No alert is required. This will surely be a rare enough event that responder won’t take it into account in his bidding. And that is the way it should be. One doesn’t have to make the call with a hand with an easy rebid after opening the long suit. I suppose if you play that you must open one no-trump when in range, that might require an alert — but that isn’t what you asked.

What do you think of this collection, with both sides vulnerable, at matchpoints? You hold six small spades, two small hearts, queen-third of diamonds and the doubleton club jack. Your LHO opens one heart, your partner bids one no-trump showing 15-18 HCP, and RHO raises hearts. Would you transfer to spades with this?

Silent Speaker, Danville, Ill.

I would not be able to transfer to spades. I would bid two spades, natural and non-forcing. Yes, this is a tad aggressive, but I want to challenge the partscore, and I can easily imagine both contracts making. I know it might not work, but I cannot stay silent when I could bid at the two-level.