Not Easy, but your Only Chance


J 8 6 5 2
A K 10 9 4
10 8
5
Q 9 4 3
Q J 6 2 7 3
K J 9 5 6 4 3 2
8 6 4 2 J 10 9 3
A K 10 7
8 5
A Q 7
A K Q 7

Five declarers were in an easily makable 7 spades and one in 7 no. My first impulse was to say that the lone declarer in that highest of contracts didn't have a ghost of a chance. And then it leaped to mind. You have that ghost of a chance on the favorable placement of the heart honors plus a squeeze. You don't wanna take the diamond hook, not because we can see it's off but because that only gives you a 12th trick and you're still going to need some luck in hearts. So you'd better eschew it and go for the suit that allows 13 tricks (with a bit of luck).
The problem, of course, is that though both heart honors are placed favorably, you don't have enough hearts to take as many finesses as you'd like. West can split his honors on the first or second heart lead. It doesn't matter. You can't pick up both his honors on finesses alone. Well, anyway, in for a penny, in for a dollar, declarer has to screw his courage to the sticking point and lead a heart, finessing the 9 or 10 if his RHO goes low, and perhaps feeling a bit optimistic if West splits his honors (though that doesn't prove anything just yet). Now declarer has to run all his top winners outside of hearts, ending up in this position:
------
A 10 9
------
------
------ ------
J 6 ?
? 6 4
------ J
------
8
Q
7
If he hasn't see a heart (or king of diamonds) at this point, there's no squeeze but that doesn't mean declarer is dead yet, since West may have had only one guard to the Q J. However, West had two guards to those honors, and with three cards left, declarer will have seen either a heart or perhaps even the king of diamonds, as West sees what will happen with throwing a heart guard and not knowing who has the diamond queen. If that queen isn't high, declarer takes a second heart finesse and has his contract.

In essence, declarer can play either defender for the king of diamonds. He starts with hearts, West splits his honors, declarer comes back and finesses again, then goes for the drop, but that doesn't work. He can now go for a 13th trick on a diamond hook. We can see that wouldn't work, but I don't know that the odds would be appreciably different from the squeeze.
So it's a dicey squeeze, needing a bit of luck in the heart suit and compounded by the possibility of an alternate line just described. Still, from feeling that declarer wouldn't have a ghost of a chance and then thinking not many would find that squeeze in play, I've gotta believe top-level experts would find it, not because it leaps to mind but because it's about your only chance in 7 no. In six no, one would surely find a better chance of a 12th trick here on a double hook in hearts, only here expecting to lose once, and pick up four tricks in the suit on a second finesse and a 4-3 split (the honors also split, of course). When our "top-level expert" found both heart honors favorably placed, he just might find his way to the squeeze.

Footnote: There's also a squeeze in a spade contract, which I also didn't see for awhile. When I noted that one declarer ran three rounds of spades immediately and so couldn't get two heart ruffs in the short hand, I thought only a defensive error had allowed him 13 tricks. But no. This declarer cashed his high hearts, ruffed a heart, cashed his club winners, ruffed a club and led a fifth round of spades. After these 11 tricks, declarer held a low diamond and 10 of hearts in dummy and A Q of diamonds in the closed. So West was squeezed. He could see that only he could beat the 10 of hearts and so had blanked his king of diamonds. After all, his partner might hold the queen. But that wasn't to be and declarer guessed right. Well done all around.