By Kitty and Steve Cooper
When you have nine trumps missing the QJxx and play small to the king, what do you do when the jack appears on your left. Do you finesse coming back or play for the drop? Is it any different if you see the queen rather than the jack?
The answer is to finesse on the way back, whichever one you see. Last month we told you to play for the drop when you were missing Qxxx. Why is this different?
In “Nine Ever” the reasoning was that a specific 2-2 is more probable than a specific 3-1 and those are the only two cases left at the decision point. The actual probability of a single 2‑2 is 6.78% and a single 3‑1 is 6.22%.
However in this case, when your LHO holds QJ doubleton he can play either the queen or the jack, they are equals. When he holds Qx, he will always play the small one unless he has missorted his hand. Because he had no choice in which to play, his choice was restricted.
If we presume that with QJ he randomly plays one or the other, then only half the 2-2s are left at the decision point once he has played the jack or queen. Even if he plays the queen more often than the jack, the half a percent difference favoring the 2-2 is gone, so the drop is no longer the favored play. Therefore the odds on play is to finesse against the expected Jxx (or Qxx) on your right. Since his play is only “restricted” with a singleton, this position has received the name “restricted choice.”
Can it be applied to other cases? Sure. Consider this case. Eight trumps missing the Q10xxx with no finesse positions, but when you play the king, the queen drops on your left. Now you can finesse the nine and lose no tricks in the suit.
But sometimes the nine loses to the ten because your expert opponent with Q10 doubleton made a great falsecard! The lesson for declarer is to start with the ace not the king so that the position is not clear to the defender. Very few defenders are up to this falsecard.
Whenever the two cards in question are equals restricted choice applies, but always beware the falsecard. Suppose you are missing J10xxx and the jack or ten drops when you cash a high one with a holding like this:
Your RHO may randomly play the jack from J10x and now how do you feel when you lose to his ten? If you like math, you can compare the odds for a singleton jack (2.39%) to half of the cases of the J10 (3.39%), much less when the J10 are tripleton (longer does not matter) and see why you should not fall for this one.
Another important point is that if the suit in which you are considering a restricted choice play is not trumps, you may be able to get a good count on the hand and learn that the suit really is 2-2 before making your play. Of course, it helps if you can count well. In a recent event, I slightly miscounted and played for the drop and was wrong. The look Steve gave me inspired this column.
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