The answer to:
KQ10987
32
A few of you either got this right or came close to getting it right. Well done!
I am making the assumption that the defenders will always defend optimally.
The first problem is whether to play an honor from the dummy on the first round or finesse the 10. This is pretty much a math problem and since some of you did the math already, I am not going to go into it here. Playing an honor from the dummy on the first round is correct.
Now let's assume that this wins the trick and you travel back to you hand to play a 2nd round of the suit with LHO following small again.
At first glance this appears to be a pure guess. Playing the other honor is necessary when LHO started with Axx and playing the 10 is necessary when LHO started with Jxx. The odds of these 2 holdings are exactly the same so it seems that you might as well toss a coin.
Now let's back up for a minute and suppose that RHO had won the first trick with the Ace. This would appear to be a bad play from Ax since RHO could have ducked and given you the guess on the 2nd round that I referred to in the previous paragraph.
However, it would be necessary for RHO to win if he had AJ doubleton since this would be his only chance to win a 2nd trick on defense.
Therefore, it seems reasonable to conclude that if RHO wins the first trick with the Ace you should play him for AJ doubleton because we are assuming optimal defense.
But is that really optimal defense? Suppose that a tricky RHO figures this out and decides to win the first trick at least some of the time from Ax in an attempt to make it look like he has AJ.
The correct strategy for the declarer is to let him get away with this, to play him for AJ, and to go up with the other honor on the 2nd round (thereby failing to win the 5 tricks that are required).
In order to see that this is true, you have to understand something about the basic nature of suit combination problems. The general way to approach these problems is to come up with a set of holdings that the defenders can have for which success is possible regardless of the strategy that the defense chooses to adopt. Several of these sets can be constructed for most suit combinations - the one you are looking for is the set that has the greatest total probabality.
So before you play a single card you should think to yourself: I can come up with a plan that works whenever RHO has Jx or AJ (among other holdings which all cancel out): I will play low to the King and, regardless of whether that loses or not, I will play low to the Queen the second time.
The alternative plan is to play low to the King and, regardless of whether that loses or not, finesse the 10 the second time. This plan works whenever RHO has Ax but it loses to his AJ doubleton.
The odds of Ax and Jx are the same so the first plan is correct because it picks up one additional holding: RHO having AJ.
Do you find the part about "regardless of whether it loses or not" to be strange? Shouldn't the defenders plays impact your strategy?
No! They are not on your side!
Make your plan and stick with it.
I hope that the above explanation was coherant. These concepts are not exactly easy to explain, but I can tell you for sure that I know I am right
Fred Gitelman
Bridge Base Inc.
www.bridgebase.com