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Playing in Palm Springs, regional KO, your opponents are Billy Miller (LHO) and David Grainger (RHO.) At the other table all four players are solid. Here is your declarer problem.

North
Q108xx
A10x
5
QJ75
South
A
Kxx
AKJ84
10642
W
N
E
S
1
P
1
P
2
P
3
P
3NT
P
P
P

The opponents are playing standard and the opening lead is the 9. You win in hand (playing for RHO to hold QJx) and play a club to the Q and K. The Q is returned which you win in dummy to play the 7 to your T and LHO's A (RHO following.) LHO plays a third heart to RHO's J. RHO produces the 13th heart (boo) on which you discard the 4 and Billy plays the J. RHO plays a spade on which LHO plays small.

You have arrived at the following position:

North
Q108
5
J5
South
AKJ8
64

Time to make some assumptions. It looks like diamonds are 3=4 or 4=3. There are a total of 70 combinations, only one of which, RHO with QT9, would allow you to make 3NT. 35 out of 70 times, if you finesse the J, you will go down two, 34 out of 70 you go down one and one out of 70 you make.

If you assume your counterparts have stopped safely in a partscore, your expectation for down one is likely to be lose 5 imps, for down two is lose 6 imps, and making 3NT is win 7 imps. Your expected value in finessing is

.50×(-6)+.486×(-5)+.014×(+7)=-5.35.

Do you take the .35 of an imp Billy is giving or do you credit him with having played the J from something like

West
KJx
98x
7xxx
Axx

(I will post what worked in a couple of days. There is no way I know of to post a poll and have a second page after you have responded to see the "answer.")

I cut my losses and power out the spade trick.
I finesse the J. I could not live with myself if I didn't and 3NT was making

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