Counting Winners, Counting Losers

J 7 5 3
J 10 5 3
8
A K 8 6
8 2 4
Q 7 6 K 4 2
J 10 7 6 A K 9 5
10 7 5 4 Q J 9 3 2
A K Q 10 9 6
A 9 8
Q 4 3 2 Contract: 6 spades
------ Opening lead: various

Counting winners, counting losers. Traditionally declarers count losers in trump contracts, winners in no trump. I would argue that counting winners even in trump contracts would be more effective, largely because it would give you some idea of how to play the hand, and counting both would be still more effective. But of course, there is the time problem in the moderate haste of play, and it would seem that counting losers in trump contracts is here to stay in no small measure, aside from habit, because there are (by and large) fewer tricks to count. Ultimately, it doesn't make any difference -- that is, it doesn't make any difference if you're good. But if you're not, the count of losers can be and often is misleading.
The recurrent mistake declarers make in counting losers is to count from a shortage in one suit in the closed hand and from a shortage in another suit in dummy. Oh, if you're loaded for bear in trump, it'll probably work. But it often won't also. Here I have given a hand where an incautious declarer, looking at a singleton spade opposite the ace in dummy, solid clubs (3-3), and two small diamonds in dummy opposite four small, announced after one trick, taken with the ace of spades, "Drawing trump and conceding two diamonds." The problem was that trump were splitting 4-0 and so after drawing trump he would have to lose four diamonds.
I see this mistake rather often. Of course when declarers boot a contract, you can't always be sure of what they were thinking, but last night, I saw what was perhaps the second most explicit instance of that mistake. This declarer, missing the top two diamonds in a 6 diamond contract, four diamonds in dummy, 5 in the closed hand wanted to claim for down one after only a couple of tricks. Every suit was solid: the top two clubs opposite a doubleton, an extra heart trick on queen-low opposite A K five times and a void in spades. There was a similarity with the first hand cited in that had trump split 2-2, she could have reaped that many tricks and the claim would have been vindicated, even though not warranted from what she knew. But trump weren't 2-2. They were 3-1, and if her RHO pumped out three trump leads, which he in fact did, she's down 2.
After the opening spade lead, which she won with the ace, she had 3 small spades. One can be ruffed and one can go on the third round of hearts, and indeed, had hearts also split evenly, she would have had her 11th trick. But that suit was splitting 6-0. Anyway, she claimed for down one. The defense declined to accept. After one more trick, I believe, she claimed again and seemed nettled that the claim was not accepted. But the defense was right. Three trump leads meant she was down two. Yes, with a void in spades in dummy and four trump originally, she did have a spade loser.
So . . . if you want to count losers, every card in one hand OR the other must be accounted for. Every card in the closed hand, for instance, must either be a winner, or played on a winner in dummy or accepted as a loser. Sometimes it's easier to count out a hand from dummy, which I have discussed and given instances of here. But you must stick with counting from one hand or your count may prove bogus.
On the above hand, 9 made slam and two went down, though the slam is unimpeachable if played well. Further, of those not in slam, a fair number made only 11 tricks, which may not be so terribly important, but maybe is for what it indicates about that declarer's level of play. Well, let's look at the hand. You've got two low hearts and 4 low diamonds (though the possibility of ruffing out the A K shouldn't be dismissed). One diamond can be lost, and indeed, must be even without a diamond lead. But the other five low cards must be taken care of with winners in dummy. Or they'll be losers.
Since you can't ruff a heart, you'll sluff two low hearts on the A K of clubs. And since you can ruff diamonds, you're going to have to ruff three times. What if declarer got two trump leads? I wondered about that when I didn't have the hand before me. That would queer the slam, whether any defenders found it or not. But you can see that the defense cannot lead trump twice (the hand with two trump can't beat the Q of D)-- and by extension, can see that you should not do so before getting your 3 ruffs.
Here's how the two slammers went down, one at trick one, the other at trick two! One declarer got a heart lead, the king drawing the ace. Declarer played the queen of spades, and now couldn't make the hand. There's only one way to play the hand on a heart lead, which is a spade to the jack, sluff two hearts on the top clubs and lead a diamond. When declarer played the queen of spades, his only quick entry to dummy to sluff heart losers is another trump lead, and he's going to find that even ten trump won't save him from losing a second diamond, though there was only one in dummy.
The other declarer got a club lead, which he took in dummy, sluffing a diamond. Sluffing a diamond! Now he can't sluff two hearts, of course, and the contract could not be made.
Incidentally, you might note that declarer is lucky in a few other ways besides the defense being unable to lead trump twice. If on a heart lead, declarer uses the jack of spades to sluff two heart losers, his LHO will have a higher trump than dummy. But West has four diamonds also and so cannot ruff. Also the clubs: If West had only three, declarer can ruff the fourth round high but West could discard a diamond. Declarer only need make sure that in backing and forthing he doesn't lead a fourth round of hearts, a suit where he held 7 originally as opposed to 4 clubs.