This may require further thought. After the 3-2
split, a working
finesse will bring in the contract. There is an issue if N has all four
but it is solvable. After the third
. lay down the
9. If it's covered, great, the
easily run. If not covered, play small from the board. S shows out repeat the finesse, you are now on the board but a
back to the hand allows you to lead the third
from hand and bring in the suit. You toss the
on the last
and lead the last
, making the hand. So if the
K is onside then, after the 3-2
break, the
finesse brings in the hand.
Now why might the
finesse be preferable? Well, to get to the board we have to play a
to the A, right. How else? If either player has a stiff K then the
come in. And if not, there is always the
finesse. Or is there?
Suppose the
K does not fall and suppose the
king is onside. We lead the
Q from the board and S, if alert, covers. We take the A and now we have two good
but we are in hand with the T3, the J on the board, and no way to get back and forth. Ok, that's a solvable problem, maybe. We only cash two rounds of trump, we play a
to the A, if the K falls we cash the last trump and run the
as above. if it doesn't fall then we lead the
Q, it goes Q K A, back to the J, trump back to had,
T throwing the
, lead the
8 and claim.
but there is a potential problem. When leaving a trump out, the
to the A might drop a stiff K, but it also might be ruffed. So we need to look at percentages. I'll use
http://iac.pigpen.org.uk/Articles.php. A 3-1 split happens 50% of the time, any of the four cards is equally likely to be the stiff, so we have a stiff K 12.5% of the time. A 4-0 split happens 10% of the time, and even if it does it's (barely) possible that the person with the !c void only had two
. This last item is not likely a priori, and usually we would have heard from an opponent if he had 11 cards in two suits, so we can probably drop that possibility. But it does seem like we have a 12/5 % shot at dropping the K and only a 19% chance of the A being trumped if we take only two rounds of trump and the play a
to the A. We succeed if the
K falls, we succeed if the A isn't ruffed and the
K is onside. I am also ignoring the possibility that the second round of
will be ruffed.
So i think the line of: Cash two trump,
to A, run the
is slightly superior to the line of: Cash three trump and run the
. Not much superior, but slightly. But the reason is not that a successful
finesse might not suffice to bring in the contract. If the
K is onside, the contract comes home if we draw the last trump and run the
9.
So I think. Maybe I have missed something.
Added: I was a little quick about probabilities, more care is needed.
After T3, having won the
and cashed two
, all following, I considered two lines:
Line 1: Cash the third
and run the
9. This always brings in the contract if the
K is with N and always fails if the
K is with S. Even if N shows out and declarer goes up with the A and goes after the
, the transportation is such that we cannot get rid of the
. So this line seems to have exactly 50 % chance of succeeding.
line 2. at T4 lead a small
to the A. This succeeds if the
K is stiff on either side, and it succeeds if both defenders follow low and the
K is onside. This is where more care is needed. We calculate the probability of each and add them since they are mutually exclusive events, call them 2A and 2B.
2A: Stiff K dropping is, as mentioned, 12.5%.
2B: Both will follow low if the suit is 2-2, that's 40%, and it will happen if the suit is 3-1 and the
K is not stiff. That's 37.5%. So both will follow low 77.5 % of the time. Now, in this line, we still need the
finesse to work, and that will happen half the time.So we take half of 77.5 and get 38.25 as the percentage for 2B. We add the percentage for 2A to the percentage for 2B and get 12.5+38.25 which gives us 50.75 %.
Conclusion: The odds for line 1, cashing the third trump and running the finesse, are 50%, the odds for line 2, leaving the third trump out and playing a
to the A, are 50.75%. Ok, 50.75 is bigger than 50.
Note: We could say that the odds for line 2 are slightly better, since it might also work if
are 4-0. That's providing the person with the
void doesn't have the third
. Yes, that's possible, but that gives him 11 red cards. Pretty unlikely, and also we might have heard from him in the auction. So maybe make it 50.75% plus a little. Very little I think. Line 1 seems to be a straightforward 50%. Also, if we get into unlikely distributions, the
could be 7-1 in which case, in line 2 where after
Q K A we lead back to the
J it gets ruffed. So all in all, I guess it's 50.75% and then plus or minus a little.
A final point: Of course no one except maybe a computer program does all of these calculations at the table. But the original justification for preferring the
finesse, namely that the
finesse might not suffice even if it is working, seems to be simply wrong. If the
finesse works, that would bring in the hand. So, unless I have missed something, the only way to prefer the
finesse is by going through all these calculations. It gives the added chance of dropping a stiff
K but there are downsides that have to be evaluated to see if it is worth it, and it's close.
