[EricK]

Here is a hand I saw presented as a problem for, I guess, beginners/Intermediates

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West leads ♥J and the suit breaks 4/4 with East having ♥AK75. West now switches to ♠J. How do you play the hand?

The solution basically said that we need 5 tricks from ♦ and the finesse at 50% is better than the 3-3 break at 36%. It did mention that the finesse is not quite 50% to make the contract because of the possible 5/1 split but this is even less likely than usual after the 4/4 ♥ break.

But it seems to me that the two lines are much closer than that. Not only does the 4/4 ♥ break make a 3/3 ♦ break a little more likely, there are various clues that the ♠ are breaking as well (West leads ♥ rather than ♠, East didn't overcall 1♠) which will push the odds of a 3/3 ♦ break higher; restricted choice suggests that West is more likely to be 3/4 in the majors than 4/4, and on hands where East has ♦Jx, he is likely strong enough to have made a take out double.

So what do you think the relative chances of the two lines are?

[Mbodell]

EricK, on 2011-November-13, 05:37, said:

So what do you think the relative chances of the two lines are?

Assuming you win the spade K and then cash the club KA and both players follow you know both players have 1 spade, 2 clubs, and 4 hearts for 7 known cards. The odds of 3-3 diamonds when both players have 6 vacant spaces is 43.29%. If you assume that both players have at least 2 spades you get 5 vacant spaces and the 3-3 split is now 47.62%, exactly as likely as a 4-2 split. If you "know" that spades are 4-3 in some direction, so both players have at least 3 spades (so only 4 vacant spaces each for 6 diamonds, a spade, and a club), then the 3-3 odds become 57.14%. With only the 7 known cards the odds of a 1=5 diamond split are 3.9%. A 0=6 break is another 0.11%. So in the 7 know cards, before even counting if E would act with enough points, the finesse is only 46%. In the 5 vacant spaces the finesse is 47.62% - exactly the same as the drop. And in the 4 vacant spaces the finesse is 50%.

[Free]

Playing ♣AK before the ♦ decision risks going down 3 if you guess the ♦ position wrong. Is this really worth it?

[whereagles]

I didn't go through the numbers, but as a rule when one side suit breaks, the odds are that the other side suits will break as well. This hints at playing from the top.