vul vs vul
But for probabilities, I was thinking of a priori. For actual play selection, I would assume that you would make the sort of adjustments to your plan that coincides with the considerations you mention.
And at least one finesse will work (unless BBO placed the Q in both hands like someone did to Hal Sims in the early days of contract bridge).
I will post the full hand in a day or so.
A priori? It could be done but it would be a challenge. But let me describe how it is done.
Let's take the line where you start be laying down the spade A and then continuing with other tries when that does not work. The overall plan will fail if all three lines fail. The idea then is to calculate the probability of failure at the probability of failure at the, the multiply be the probability of failure at the next step, the multiply by the probability of failure at the third step. But things split, there is more than one way to fail At the first step, laying down the spade A, this fails if the K does not fall. But maybe the suit is 3-0, maybe the suit is 3-1 but the K is not falling. Which way failure occurs has a modest effect on the probability of failure at the second step. For convenience, we will treat the second step as independent of the first step. This means that we just ask "What is the probability of bringing down the
A in three rounds of diamonds, w/o knowing anything about how spades are arranged?"
So:
Te probability of a 2-1 break in spades -7 0.78, and one third of the time the K is stiff, so the K falls under that A with probability 1/3 of 0.78 0.26. Which means the probability of the first step failing is 0.74.
Now we go on to the second step. What is the probability of bringing down the
K in three rounds of diamonds? Ah, but it is not so simple. If we lead a diamond and then ruff a diamond, it might be over-ruffed (with a higher spot, which can only happen if spades are 3-0, Rho holding the trhee) and then we are down, we never get to the third step. But let's ignore that. So the probability of a 4-3 split in diamonds is 0.62, the probability that the K is on the three card holding (we don't care whether E or W) is 3/7 of 0.62, a little under 0.27. So the probability of step 2 failing is 0.73.
So now the probability of both steps 2 and steps to failing is obtained by multiplying 0.74 by 0.73. I get about 0.54.
Now things get complicated.
You say at step 4 you will cross to dummy and finesse [against] the
Q. But now we really have to look at whether spades split 2-1 or 3-0. If they split 2-1, no problem and the diamonds have split 3-4, no problem. And we have to look at which spade we ruffed that third Not if they diamond with. If we ruffed low, there was a real danger [well, maybe not that big a danger, W should have at least three so maybe we ruffed low, but we are getting away from a priori] of an over-ruff. So we ruffed high. But now if we lead a diamond it can be over-ruffed. So play a spade first? Not if spades split 3-0 We have cashed the spade ace, we have ruffed two rounds of diamonds, so there are two spades left in dummy. If we lead a spade the K wins and another spade is led. Even of hearts split we will be losing a diamond.
So assume spades were 2-0, but that changes how we view the probabilities at step 1. Anyway, assume it, Then we ruff a diamond and take the heart finesse, making if it succeeds. In some a priori sens, that's a 0.50 shot. So the probability of failure is 0.50 times 0,54 which is 0.27. But it really isn't that good because of the 3-0 spade problem.
So more is needed. And I have been a bit casual about some technicalities.
And then a priori is really not the way to go anyway.
My thinking for my route is that the second
will not be over-ruffed on my right. This is because it would give Lho six diamonds, and so even if he also had six clubs he then would have bid 2NT rather than 2
. And I don't careif Lho is short in
, if he ruffs it has to be with the K if it is to stand up. So it is safe to fist duck a
and then ruff one small in dummy. After that, I lead a spade from the board. I did not really get into what I would do if my Rho shows out, but if he plays low then I play the Q. Firstly the finesse might work, secondly if the finesse fails the I know the spades are not 3-0. So I think that this is a better start. But I did not calculate the probabilities.
And I am definitely not sure it is best.
I did now look up the hand, couldn't bear the suspense, so I know whether or not it works.