Which Finesse?

West leads the ♦ A and his partner contributes the four. West shifts to a trump, and you draw trumps in two rounds ending in hand, then lead a club to the queen. East wins the ace and leads a heart. Should you take the heart finesse at this position?

The contract is in the bag. The question is, how can you make the overtrick? You have two clubs, a diamond, a heart, and four spade tricks. East has cruelly made me make the red-suit decision now, it seems.

The heart finesse would be 50%, but it is slightly better than 50% that the ♥ K and the ♦ Q were in different hands. You play the ♥ A, cash the ♦ K and run the spades, pitching a diamond and the ♥ Q. You reach this position: If the red suit honors were split among your opponents, then neither could hold three clubs at this end position. Even if they weren't split, if the person with both honors also held four or more clubs at the beginning, you'd still have that person squeezed. This makes this line much better than 50%.

Sometimes, when presented with a choice of two finesses, you should choose neither.

Technically, this isn't a double squeeze, in that only one person is guarding clubs. Still, it operates like a double squeeze.

Incidentally, I found this play at the table, but when I cashed the ♦ K, East's queen dropped. East also held the ♥ K and long clubs, so anything I did, short of taking the diamond finesse, would have given me the overtrick. The full deal was: West could put pressure on me by continuing diamonds at trick two. If he had, I had already decided to fly the king, to avoid losing four tricks on the hand.

What happens if, after winning the ♣ A, East exits a club? That then kills the entry for the squeeze above. Instead, you win the club return, cash the other top club, the ♦ K and run the spades. The end position is: On the last spade, if East doesn't pitch a club, you pitch the club from hand. If neither opponent pitches the ♦ K, you play the heart to the ace, hoping that one of the opponents was forced to bare the king.

This line fails whenever West has the long club and exactly one of the ♦ Q and the ♥ K, or if he holds the ♥ K and no other control. If either opponent has the ♦ Q and the ♥ K there is an automatic squeeze. If East holds the ♥ K and the long club, there is a positional squeeze.

I think this all adds up to more than 50%, but it's difficult to tell given all the different pieces of information you have so far - for instance, if East has the ♦ Q, why didn't he signal a clear encouragement? Tough to figure that kind of thing into probabilistic analysis.

What happens when West hold the ♣ A and wins the second club? Obviously, he'll want to exit in clubs or diamonds. If he exits with a diamond, you play the ♦ K, cross with the trump ten, cash the ♣ J, pitching a heart, then run your trumps. This reaches the 3-card ending noted above.

Paul Wendt has noted that the defense can break the squeeze if they hold up the ♣ A twice. This gambit gets rid of my club loser, but it fails to give me any more winners, and it keeps me from rectifying the count for the squeeze. My best bet is to try both of the red-suit finesses. If one of them is on, I've got my overtrick. If both are on, I've got two overtricks.

But why on earth would either opponent duck the club twice? I'd be dealing either with an act of either extreme cunning or extreme stupidity. Maybe my opponent is aware that both finesses are offside?

If both red honors are offside, I can only make the overtrick, double-dummy, if East is holding the ♣ A, via a strip squeeze at this end position: On the last spade, East clearly can't part with a diamond or the club ace, so he must part with a heart. Now I cross to the ♥ A and throw East in with the club.

Perhaps it is right, given that one of my defenders has brilliantly held up the ♣ A, to play for both finesses offside. Or maybe that's just what they want me to think. I would certainly start feeling quite paranoid if they ducked clubs twice.

Still, I don't anticipate too many defenders will find that defense. I know I wouldn't.