Interactive Problem 11

East cant hold up with KTx, they risk blowing a trick when partner has the queen. I mean they could its just wrong. If they do hold up it only costs you when the king of spades is offside. Thats quite unlikely. They had to make a bad mistake and then you lose another finesse. As far as the percentages. This isnt my specialty, but I'll give it a go. I am making an assumption that the numbers you presented are correct. Double finessing picks up KT6, KT5 (those two combine for 12.15%, which is 1/4 of the 3-1 breaks) and KT65 which is half of the 4-0 breaks (4.5%), so double hooking will do a trick better 16.65% of the time. Playing the 8 to the jack, picks up K6, K5 (1/4 of the 2-2 breaks, 10.25%) + singleton king onside (1/8 of the 3-1 breaks= 6.25%). so 16.5% So in a vaccum because you have the 7 of clubs, it may be slightly better to double hook, however this is missing a key point. They didn't balance. A hand that has AK of diamonds + a club void would almost certainly balance. If they had a singleton club they are much more likely to balance. So this swings the odds significantly in favor of playing for 2-2. I dont process all this at the table, I just know from experience its better to play to the jack. In fact the best play is probably the 9 of clubs, because they may cover with KT6, hoping partner has Q8(x). If they do that it swings the odds significantly.

Don't forget that 3-1 is only more likely than 2-2 because it includes both 3=1 and 1=3. If you take the spade finesse back, then on playing the second club and seeing LHO follow, 1=3 is no longer possible.

I think the odds in Gavin's post are off. Playing towards the J is also mathematically better in a vacuum: The double finesse calculation is correct. However, playing 8 to the J picks up K6 an K5, which is 1/3 (not 1/4) of the 2-2 breaks. Furthermore it picks up an extra trick with KT offside (it won't lose twice) for another 1/6 of 2-2 cases. This makes 1/3 + 1/6 = 1/2 of the 2-2 cases for 20.5%. I'm not sure why the singleton K onside is considered. In both lines West must play it and it will be captured by the A. The inferences Gavin mentioned point even more towards finessing the 8 to the J. Even with East wrongly ducking the trick, you will discover it when you cash your club A and you can still choose to take the spade finesse.

Yes youre right my percentage for the 2/2 breaks was wrong , I will edit it to show the increase. Singleton king is very relevant. If you lead the jack you are losing a trick to the ten. Playing the 8 to the jack, picks up K6, K5 (1/3 of the 2-2 breaks, 13.66%) + singleton king onside (1/8 of the 3-1 breaks= 6.25%). so 19,91% So yes even without the inferences it is correct to play for 2-2 rather than 3-1. With the inferences it is an overwhelming favorite. If we didnt have all of the 987 it would be even more extreme.