Count Your Winners

A J 9 7 2
A K J 9 8
A K 9
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4 Q 10 8 6 5 3
Q 5 4 2 6 3
8 7 5 J 4 3
Q 8 7 5 4 J 3
K
10 7
Q 10 6 2Contract: 6 no
A K 10 9 6 2 Opening lead: 4 of spades

Some made this contract and some didn't, even going down two, though a simple count of winners should bring declarer all the marbles when the heart finesse is on. But first, we're going for 12 tricks, not an overtrick if that in any way endangers our primary quest. Lemme take the hand first from the opening lead of a spade. That is really the most convenient lead, even better than a diamond, which guarantees four diamond winners because you can't go wrong on the J of diamonds. The spade lead means you still have all suits stopped and you've got a certain re-entry to the top clubs by way of the Q of diamonds. So let us count:
We've got two spade winners, two clubs, three diamonds (for certain) and four hearts (for certain). That adds up to 11, so our first thought is how to develop a 12th. And from there, we go after the likeliest means of gaining that winner. Both spades and clubs offer some possibility of that 12th trick with a little bit of luck, but you'd do well not to count on that luck if you have other possibilities, as you do here. For both hearts and diamonds offer another trick on a favorable finesse, or in the case of diamonds, a 3-3 split (though of course, you can't test for both diamond possibilities sequentially). But you can test the hearts and diamonds sequentially if the finesse loses. Only four heart winners? Well, we'll try for a fourth diamond. But you can see it won't come to that.
Hence, we try the heart hook, since we're in the right hand. Incidentally, declarer has to keep open to all possibilities. A successful heart hook doesn't automatically give you five heart winners, since a 5-1 split would hold you to four, and you'd have to go for a 12th trick in diamonds. So you lead your 10 of hearts. If West covers, it's all over, for you have all the spots. If not, push the 10 through, and when that holds, repeat the finesse, and with everyone following, now you have five heart winners, which means the 12th and your contract. You run your hearts, sluffing three low clubs. And you cash the ace of spades, sluffing . . . ? Well, what? You could sluff a diamond and hope for Q J tight in clubs. Or you sluff a club and look for a thirteenth trick in diamonds. You might even have East on a minor suit squeeze if only he can guard the third round of clubs and holds 4 diamonds. Obviously, the luck needed in clubs is too specialized to compete against a 50% finesse, not to mention the possibility of the J of diamonds falling short. So unless you've been seeing a powerful lot of clubs discarded on the run of the hearts, you sluff clubs, cash your top diamonds and on the third lead the jack pops up, and you're in clover.
How did anyone miss the favorable lie of the red cards for 13 tricks, not to mention a 12th, or even an 11th in a few cases. Well, lemme see. I look at one who went down one. Opening lead (played from the North hand above) was the J of clubs, declarer winning in (his) dummy, sluffing a heart from the closed hand. Sluffing a heart from the closed hand! Wait a minute. That's a winner. That's a winner even on a losing heart finesse (excepting the 5-1 split referred to above), while the spades can't possibly set up for the 5th spade to be a winner. The best you can get in spades is for a Q 10 doubleton, and that still wouldn't allow for the fifth spade to be a winner, and it's far too specialized a holding to count on anyway.
To be sure, that alone didn't queer the contract, since declarer originally had the potential for 13 tricks and has throw away only one. But the discard didn't augur well. What did he do for an encore? He cashed the K of spades, took the heart hook and continued on to four heart winners, cashed the A of spades, apparently took no note that one defender showed out, and now continued spades to his LHO's Q 10 tenace for down one. Just a ridiculous play when a simple count would have shown him that he still had hope with the clear possibility of a fourth trick in diamonds for his contract, where the lead of a spade offered none. A simple count would have left him with 3 IMP's instead of minus 12, a significant difference.
Another case with a totally ridiculous play when the requisite winners were staring declarer in the face. Opening lead was a diamond to the J and Q. This, to be sure, demands a little more thought, for entries are at a premium. Indeed, declarer has only one now to the closed hand and a number of winners to cash out before leaving that hand for the last time, and no way to avoid cashing out the top clubs before the heart hook, which must be done. Declarer has to cash the top diamonds at that point, come back to the K of spades, cash the fourth diamond and 2 top clubs and take the heart hook, where either a successful finesse or East being out of clubs after two leads would bring the contract home. Of course declarer could go down on a losing heart hook and the quick cashing of a club. But he has to do something that adds up to 12 tricks. As you can see, declarer had both favorable situations and should have come home with 13 tricks. But . . .
Declarer took the heart finesse right away! He cashed out five winners, sluffing clubs, and now he has only one entry to the closed hand. If he cashes his top diamonds right away to make the 10 of diamonds available, he has no re-entry back to the A of spades, and if he holds onto the top diamonds, he's going to lose the 10 of diamonds. Still, again, declarer has thrown away a trick needlessly, but not yet his contract, since he always had the potential for 13. He should come to the K of spades, cash his clubs, get back in diamonds and cash the ace of spades, for 5 heart winners, 3 diamonds, and two in each black suit. That's 12, no?
Instead, declarer, after running five hearts, cashed the ace of spades, gobbling up the king! That's not just a trick lost. That's about 3 tricks lost. He has no access to the top clubs now, no access to a fourth diamond winner, and of course, has just spent the top two spades on one trick! Oh, I can't go on.
Here's a declarer who got a diamond lead, also. He unblocked the suit and led away from his top hearts. As before, he's thrown away a trick, but since he started with a potential for 13, one might think there is still hope. The problem, of course, is entries. It would have been awfully nice if the opponents had led a spade here. Declarer can cash out his minor-suit winners and now get to dummy and the A of spades with a heart lead. Unfortunately for declarer, the defense returned a heart. Declarer could cash out his 4th diamond and the top clubs, but now his only entry to dummy and the rest of the hearts lies in overtaking the K of spades, and one thing he can't afford to do is to toss away a heart trick and a spade trick. Down one, through a failure to take a simple finesse, to watch entries and to count up to 12.
Lastly, here's one who took the spade opening lead and went after clubs! With all that potential for 5 hearts and four diamonds without losing the lead, he goes after a suit where he'll almost certainly have to lose the lead to pick up maybe a third winner in the suit. Incomprehensible. Since declarer actually does establish a third club winner, by virtue of the fall of the J and the 10-9 sequence, he can live with only 3 diamond winners if he'll cash his third club winner and take the heart hook. But he was fixated on those clubs, and after cashing a winner on the fourth round, he played a fifth round into West's 8. Down one.
Did he have a fixation on playing out of the closed hand? Don't know, but that's what it looks like. I wouldn't regard this as a dummy reversal so much as simply counting winning tricks, wherever they are, and that declarer didn't seem to do.