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You are declarer in 3 NT, the opening lead is the ♠ 10. You play the ace, of course, hiding the spade queen from both opponents.. The spade suit presents no danger. The opponents can easily see that their best chance for tricks is in diamonds. If you lose the lead, you will likely go down. If you can win all six club tricks, you make the contract easily.
Can you play the club suit for no losers?
If clubs split 2-2, you win by simply cashing the two top honors, easy! If either player has queen-jack-third or queen-jack-fourth, you can't pick up the suit unless they make a glaring mistake. And if the suit splits honor-third and a singleton honor...?
You lead the ♣ K. East follows suit with the eight, and West (an expert player) plays the queen in tempo without hesitating. You lead the ♣ 5 from dummy, East plays the nine.What now? Play for the drop (ace) or finesse the ten?
- If the club suit split is Q and J98, then you must finesse the ten.
- If the club suit split is QJ and 98, you win by playing the ace.
ANSWER: Finesse the ♣ 10. This is a textbook-classic example of a restricted choice situation. Although the 2-2 split is slightly more likely than a specific 3-1 split here, there is an important hint in the play so far. If West has both the queen and jack, she might choose the queen or she might choose the jack (the expert randomly chooses either card 50% of the time, see below). But if she only has one card, she must perforce play it; that is, her choice is "restricted" by the fact that she has no choice at all. The odds are almost 2:1 in favor of the finesse at this point; the finesse might not work, but it is the clearly preferred line of play.
If West had hesitated before playing the queen, that would be a strong indication that she held both the queen and the jack; play the ace! It would also be a strong indication that she is not an expert; an expert player holding queen-jack doubleton would have planned her play as soon as dummy came down. Keep in mind that it is highly unethical to deliberately hesitate before playing a singleton (see Law 73E in the Laws of Duplicate Bridge).
If West is an inexperienced player who "always plays the jack from queen-jack doubleton", then you practically know for certain that the queen is a singleton here. If she had played the jack, you would play for the drop with odds just slightly better than 50-50. Adjust accordingly if she "always plays the queen".
These "restricted choice" situations arise fairly often, almost any time you are trying to suss out two touching honors in the opponents' hands and you have to choose between a finesse and a drop play. The queen-jack, the jack-ten, sometimes the king-queen, and even the ace-king in some situations.
THE PRINCIPLE: If the opponent could have freely played either of two touching honors, there is an inference available that she is less likely to have the other one because her choice might be restricted. This does not apply to opening leads, or third hand play when trying to win the trick, because the choice of honors in those situations is determined by partnership agreements. And of course if you have other information about the opponents' hands, like known high-card points or known distribution, use that information instead.
BONUS MINUTE: The optimal play for a defender holding doubleton honors is to randomly play either card with equal probability, as this gives up the least amount of information to declarer. Note that this does not apply to opening leads or to following suit when trying to win the trick. You'll need to make your choice well in advance -- like, before playing to the first trick -- because hesitating at your turn to play will give away the store. One simple way to make a 50-50 choice is to use the number of high-card points in your hand: with an odd number of HCP, play the "odd" card (the jack is the "eleven"), with an even number play the "even" card (the queen).
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-- Ray
Better Bridge in 5 Minutes. Guaranteed! (or the next one is free)
