Grant plans to work in some probability into his talk today (9-28). We were chatting about a recent hand I held. It's a little technical so I thought I would put it up so people can come back for a later look if they like.
I will explain later what actually happened, but for now I want to focus on the probabilities
Dummy
AT9
J632
84
QJ53
Hand
732
Q8
AKQT5
AK7
Let us suppose that you are in 3NT and you get the opening lead of the
K. Never mind overtricks, you hope to take 9. No doubt you should duck a couple of spades but it's pretty likely that once the opponents get back in they will be able to take at least three spades and two hearts, so you must take 9 before they get in again. .
You have one spade trick and four club tricks, you need four diamond tricks. Five diamond tricks would be nice, but four is essential. You have two possibilities. Lead small and finesse the T, or bang down the AKQ and hope for the best. Of course if you are going to finesse you may as well lay down the A first just in case a miracle happens.
The finesse is a 50% shot.
If we lay down the AKQ, the suit will split 3-3 36% of the time. That's not good enough. However, the J could fall doubleton. Or the J might be stiff. Or it could be that all six diamonds are on you right, in which case after you lay down the A you will be able to go to the clubs and take the marked finesse.
So maybe laying down the AKQ is right?
Yes, it is, and we can do the calculation if we just have the basic precentages memorized. The chance of a 3-3 split is 36%. The chance of a 4-2 split is 48% and, when there is a 4-2 split the J will be doubleton 1/3 of the time (there are two places to put the J in the doubleton and four places in four card holding. We see that 1/3 of 48 is 16, and 36+16=52. Ok, that's better than a finesse. Not much better, but better.
How about 5-1 or 6-0? It can happen. I won't go into details here, but dropping the stiff J is is about a 2.45 % chance, and finding all 6 cards on your right is about a 0.75 % chance. So we are up to about 54%. Added: A more detailed calculation gives 54.8%
But wait! Someone with the Encyclopedia of Bridge (I have the 5th edition) might point out hand 18 in their very long list of suit combinations. It says there that the way to play AKQTx opposite xx for four tricks is to lay down the A and then finesse the ten, and the chance of success is 93%. So the new question might be: Has Ken lost his mind??? No, I have not. Our problem is to take four diamond tricks before the opponents take their three spades and two hearts. The 92 % number from the Encyclopedia assumes that if the finesse of the Ten loses, you will still have time to later go back and take the last diamond. That's not the case here. You need your four diamond tricks sooner, not later.
I promised to say what actually happened. I opened 1
, there was a spade overcall on my left and partner doubled, showing four hearts. Maybe I should have bid 2
, that would get us to 3NT but I tried 2
hoping the auction would not die there. It died there there. Well, I made 2
! Would I have liked to be in 3NT? That depends on how the diamonds behave. The spade overcall affects the probabilities, but I think it is still right to lay down the AKQ. Either it works or it doesn't.
