[manudude03]

Stephen Tu, on 2016-June-21, 09:54, said:

How you get 65%?? It is 37/76. Restricted choice already is factored in.

Maybe you mean 37/50 for the hook, 74%, looking at only the cases it's possible to pick up the suit for no losers and the k didn't pop up stiff onside already.

I said it was 74% if you consider restricted choice. And yes, I meant 74% of the time it matters you have to hook. If you ignore restricted choice, then the possible holdings you can pick up and their probabilities are :
1. xx-K: 26%
2. Kx-K: 26%
3. Kxx-v: 22%

Adding those up we get 74% of which we need to finesse on 48 of them, hence the 48/74 figure or 65%. When you add restricted choice into the equation, you half cases 1 and 3 and get the 37/50 or 74%

[Stephen Tu]

I guess I don't understand the idea of ignoring restricted choice. If we are looking at the 76 cases that haven't been ruled out by lho following suit low, we get 37 winning cases not 48. Don't see how you get to double 3-0 onside splits from 11 to 22, that's weird.

If you want to ignore restricted choice, and specify an opponent that always plays lowest, and specifically played the deuce, then the success rate is 24/37. Now if you randomly double everything, then we get 48/74 which is same ratio, and thus the right answer, but to me a weird way of counting. But your post I responded to above had 48/76, not 48/74, thus I am not sure how exactly you were counting.

And when they follow suit with the 3, then it is 13/13 for the hook when it matters so then we get back to 37/50 overall.

[manudude03]

Stephen Tu, on 2016-June-24, 08:05, said:

I guess I don't understand the idea of ignoring restricted choice. If we are looking at the 76 cases that haven't been ruled out by lho following suit low, we get 37 winning cases not 48. Don't see how you get to double 3-0 onside splits from 11 to 22, that's weird.

If you want to ignore restricted choice, and specify an opponent that always plays lowest, and specifically played the deuce, then the success rate is 24/37. Now if you randomly double everything, then we get 48/74 which is same ratio, and thus the right answer, but to me a weird way of counting. But your post I responded to above had 48/76, not 48/74, thus I am not sure how exactly you were counting.

And when they follow suit with the 3, then it is 13/13 for the hook when it matters so then we get back to 37/50 overall.

The 76 was a typo. I meant 74. As for the chances of 3-0 doubling, say we were missing K32 and LHO played the 2 on the first round. The chances that the 3 was in the LHO hand (without considering restricted choice) would be 12/25. If LHO had both the 3 and the 2, then the chances of LHO having the king would be 11/24. Multiplying those fractions together gives 11/50 or 22%.

Another way of looking at it is that the chances of a 3-0 break (either way) initially was 22%. Once you put a specific card in LHO's hand, you need to remove exactly half the holdings (the cases where that card was with RHO), which doesn't do anything to the percentages once you weight them back so the percentages add to 100% again (effectively you are halving the percentages and the doubling them again when weighting them).

[fromageGB]

manudude03, on 2016-June-24, 05:57, said:

I said it was 74% if you consider restricted choice. And yes, I meant 74% of the time it matters you have to hook. If you ignore restricted choice, then the possible holdings you can pick up and their probabilities are :
1. xx-K: 26%
2. Kx-K: 26%
3. Kxx-v: 22%

Adding those up we get 74% of which we need to finesse on 48 of them, hence the 48/74 figure or 65%. When you add restricted choice into the equation, you half cases 1 and 3 and get the 37/50 or 74%

Sorry, I am not following this. 26% of the time LHO starts with exactly 2 cards it is xx? I figure a third (33%). Anyway, total scenario with LHO playing the 2, what is the percentage chance of the finesse working? I have created a poll in "general bridge discussion", so you may care to reply there.

[manudude03]

fromageGB, on 2016-June-26, 05:28, said:

Sorry, I am not following this. 26% of the time LHO starts with exactly 2 cards it is xx? I figure a third (33%). Anyway, total scenario with LHO playing the 2, what is the percentage chance of the finesse working? I have created a poll in "general bridge discussion", so you may care to reply there.

Once LHO plays the 2, he can only have started with 2, 32, K2 and K32. Out of those, the first 3 are 26% while the last is 22%. I ignored the first of these since you have a loser whatever you do.