Posted 2012-June-26, 22:27
You can't make if west started with three hearts, so you have to play West for two or one heart. Most of us will not play him for two singletons, so lets consider the possibility where West has a doubleton heart. If he had 85 doubleton he had a choice of hearts to play, but if he had Q5 he had to play the five. So restricted choice says to play for the drop of the queen, and this is not even close. So I would play for restricted choice and pop up with the king. (well lead the king from hand).
However, that doesn't mean East can't have three hearts, but the chances of east having three hearts and five clubs to west's 1♥ and 1♣ and west not bidding seems remarkably low, but he was very weak (east had spade A and probably jack, and club ace). But to be certain that the restricted choice solution to the 2-2 split out weighs the combined Qx and Qxx on side, you would have to estimate the chances for hearts to be 1=3.
The chances for 2=2 split with the known club split, is just below 40%, the chance of 3-1 is heavier for the hand with short clbus having 3, but you can't make it then. The chances for the hand with long clubs having three is almost 14%, but you can eliminate 1/4 of those since the one with the singleton queen didn't happen, dropping the odds to about 10%.
So here is what you have, remaining....
♥x ♥qxx (10.5%) - correct for when makable = 21.4%
♥xx ♥qx (19%) - corrected for when makable = 39.3%
♥qx ♥xx (19%) - corrected for when makable = 39.3%
without considering restricted choice, the finesse line looks much better (39.3+21.4= 60.7%) than playing for the drop. However, this is where simple math falls down. When west ruffed with the low heart, there is a presumption that his choice was restricted.
However, the math is actually different. The assumption when west ruffs low, his choice would be restricted with Qx, that is, if I understand this correctly, with
Q5 - must ruff with 5 100% of the time
85 - would ruff with 5, 50% of the time
So if west had a doubleton heart, then it he the odds are something like two our three that his second heart is the queen. So of the 38% with 2/2 split, the odds would be 2/3 x .38 or 25.8% he has the queen, and only 13% that he doesn't hold the queen.. The restricted choice implications changes the table from above to this...
♥x ♥qxx (10.5%) - correct for when make able = 21.4%
♥xx ♥qx (12.2%) - corrected for when make able = 25.1%
♥qx ♥xx (25.8%) - corrected for when make able = 53.5%<br class="Apple-interchange-newline">
So when you add these up, the odds become for the finesse (21.4 + 25.1) is 46.6%, playing for the drop is 53.4%. There could be rounding errors here. These numbers are rough estimates, and i could be off a bit, but I think the wc player was probably thinking along these lines.
--Ben--