Howzzat?

Countcher Winners!

6 2
J 7 4
A K 7
K 10 8 4 3
K Q 8 J 10 5 4
K 9 8 6 2 Q 3
10 8 5 6
Q 9 A J 7 6 5 2
A 9 7 3
A 10 5
Q J 9 4 3 2Contract: 5 diamonds
------ Opening lead: diamond, heart

My first example under Counting Winners involved an incautious declarer who thought that two low diamonds in dummy opposite four low in his own hand meant that he only had to lose two diamonds. The need for trump in dummy for this to be so seemed entirely beside the point. This is a wrongheaded presumption I have seen any number of times, but this was the most explicit and glaring manifestation of it, and so it became one of my favorite hands. People who tell us what could have been made in another denomination as we tuck the cards away and mark our score are probably wrong more often than right. But you don't know which times they're wrong and which right until we look at the whole hand a little while (by and large) and when you discover their error, they're long gone.
Nor is this a totally academic matter. For people who are wrong in a hasty analysis will tend to carry this over to their play, as the incautious declarer did on the first hand. The above hand was another case of a mistaken quickie analysis, this time recognized as wrong right away by one person, but not grasped by others even with an explanation. At my table, this was played in 3 hearts by E-W, down four, and now the West player opined that (the defenders) could have made five diamonds! "It depends on the hearts", said her partner (East). "I think it depends on trump leads," said I, at which East wanted to know what I was referring to with "trump leads", as if that were some obscure concept. I said that if X (West) led trump twice [which she obviously could do against 5 diamonds], then we lose two spades in addition to a heart. (And that was without taking up how likely it would be that we would avoid a second heart loser!) The table got kind of quiet then. Nobody argued with me, but then nobody agreed with me either. No one said, "By golly, you're right, I didn't see that." It just got quiet and no one spoke another word.
Of course you can't count winners easily when the hand is gone to electronic limbo for the moment, but anyone whose impulse was to count only one spade loser here should take a moment to count winners, and you'll see it's simply not so easy to pick up 11 tricks on best defense and even picking up 10 requires a good guess in hearts. You've got six diamond winners and two major suit aces for 8. You can cash the ace of spades and lose a spade and get at least one ruff in dummy for 9. You can play your hearts so as to lose only one trick when one opponent has a doubleton honor, but the catch is to guess which one. Here, a low lead to the 10 of hearts would do it. That's 10 tricks on a good guess. And the eleventh? That can only come from a second ruff of a spade, which is only possible if diamonds are not led twice by West.
So it is evident that 5 diamonds is impossible with best defense and chancey if the defense doesn't get around to leading trump.

Footnote: I later decided to go back and see what the field did, which was: six people bid and made 3 no here (another contract that cannot be made with first-rate defense). No one bid and made 5 diamonds, and only one person (in two diamonds) picked up 11 tricks in that denomination. One declarer was in four doubled, a makable contract on any lead, and doubly so when this person got a heart lead! That takes care of a second trick in hearts, and it only remains to get one spade ruff to make for a very nice score. A bit of counting should have settled her mind. She has six diamond winners, two hearts and the ace of spades for 9. One spade ruff makes 10. Cash the ace of spades and lose a spade. What could stop her at that point? Unfortunately, she wasn't given to counting and in effect fell on her face by going for an overtrick, thus:
Heart lead to queen and ace, ace of spades, switch to a diamond to the ace. (That was a shrewd play, since losing a spade here would give the defense the potential to ruff out the third round of hearts. Declarer can afford exactly one trump lead.) A spade back to the 9 and king, a club from West ruffed, spade to the 7 of diamonds. That was a "subtle error", though not a fatal one. She might have been overruffed, and facing a trump return for down one, when she could have guaranteed her contract -- a doubled-into-game partial is no contract to treat lightly -- by ruffing with the king and coming back with the 7 of diamonds to lead out trump with the Q J and then establishing a second heart by leading the 10. When she wasn't overruffed, she again could have guaranteed her contract by cashing the king of diamonds and then, with one trump out and the top two in her hand, ruffing a club high and to draw the last trump and claim. Either of these ways would have given her a second spade loser, but since she has only one heart loser, what of that? You don't want to jeopardize 4 diamonds doubled by going for five, now, do you?
Anyway, here's what she did: She ruffed the second round of clubs with the queen (!), ruffed her last spade with the K, and now was overruffed on a club lead back. West cashed his king of hearts, (she still could have made it by playing the jack under the king, which would have allowed her to win the third round of hearts in the closed hand to draw the last trump), and conceded the third round to the jack. Another club lead was overruffed! She may have prevented a second spade loser, but with the top four trump on a 9-card holding, she lost a trick to the 10 of diamonds and another to the 8! The first overruff was tolerable because she took one more spade ruff in dummy than necessary. The second was the setting trick.