How many extras does an overcaller need to double for take-out, then double again? One of our opponents followed this sequence with perfect 4-4-4-1 shape, but just three aces and a queen. His partner passed with queen-jack-fourth of trump and a king, but couldn’t defeat our contract. Does the second double promise more cards than this, even if it is still for take-out?

Reopen for Business, Edmonton, Calgary

When a hand that has doubled for takeout bids again, it shows extras. The second double is still for takeout, though this one may come close to being played as optional, depending on the level of the action, say a double of a game contract. In such situations, sometimes responder passes from weakness if balanced, and hopes for the best.

I enjoy your bridge column and tend to go along with most of your views on bridge. But recently, you featured an opening bid in third seat when holding ♠ Q-J-9-2, ♥ A-9-2, ♦ J-6-4, ♣ K-3-2. I do not enjoy opening one club with this hand; I’d rather open one spade and plan to pass any non-forcing response. Where do you stand here?

Trumpet Voluntary, Palm Springs, Calif.

I agree with you that a one-club opening bid does not accomplish much. Passing is perfectly reasonable, and when I do open a minor in third seat, I tend to have either a good suit or a reasonable hand. This hand does not qualify as either. A one-spade opener is more pre-emptive and lead-directing, so that would be my choice.

You recently discussed the Principle of Restricted Choice. Please explain how the concept works and when it applies.

Monkey Wrench, Newport News, Va.

Occam’s Razor basically says when you have to weigh up two outcomes, go for the simplest. So, when you have to compare the chance that a player has a doubleton consisting of two equal cards (generally the queen-jack) or that they started with a bare honor, the latter is more likely. The doubleton is more likely than each individual singleton, but the chance that the queen will appear from the doubleton holding is actually only half that, because half the time the player would contribute the jack from queen-jack. See details of “The Monty Hall problem” online.

What should persuade responder to upgrade a constructive raise of a major to a limit raise? For example, if you hold ♠ Q-9-2, ♥ K-7-3-2, ♦ J-6-4, ♣ A-3-2 and hear your partner open a major, would you make a simple raise or a limit raise of one heart or one spade?

Shark Tank, Key West, Fla.

You have a 10-count, but it is too balanced to make a limit raise of one spade. Make the club ace the diamond ace, and you might consider the limit raise; but since partner typically has a balanced 12-14, do you really need to be in game facing that? I’d simply raise to two spades. By contrast, the fourth trump would persuade me to make a reluctant limit raise of hearts, even if I’m not convinced the hand is really worth it.

You recently featured a deal where someone in second seat overcalled one heart over one diamond with a six-count, when holding ♠ 6-3, ♥ Q-J-10-8-4, ♦ Q-J-9-2, ♣ 6-3. I have seen this sort of action several times, both at the table and in your column, and I wonder where you stand on it.

Hot Drinks, Indio, Calif.

To clarify my position; I was just reporting the facts. This hand is not exactly worth an overcall. If I had to put a point-count limit on one-level overcalls, it would be a decent suit in a hand of 8-9 points. In the example hand, I would happily overcall if one of the queens were an ace.