How Many Heart Winners?


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

I had to reconstruct this one from memory, since I can't find it in my papers. So the spots may not be true, but I do remember the salient features. The hand surfaced right after I had a tentative page on "eight ever, nine never" and how two cold contracts had been butchered by ignoring that advice. Here it wouldn't seem to work. Or doesn't it? (-- if I may be allowed to treat a 7-card suit as offering all the more reason than an 8-card to finesse against a queen.)
How many heart winners do you need on this hand? No, we see that you can get by without any heart losers. But the goal, once the contract is established, is not to avoid any heart losers but to avoid two losers. So it would seem that if you pick up the Q of trump, you can afford to lose one diamond, and hence can get by with three heart winners. But if you go for the drop in clubs and hence have a club loser, you're going to need four heart winners to sluff two diamonds from the closed hand. And how do you get four heart winners?
Well, from declarer's viewpoint, without knowing how the cards lie, there are three basic ways: Dropping a doubleton queen sitting after the A K, finding a 3-3 split, ruffing out the third round, and lastly, finessing the J of hearts first round and playing for, well, the cards as they are. Which way is best? Well, the odds would seem to favor the third possibility. They definitely favor a 4-2 split over a 3-3, and if there is a 4-2 split, the queen figures to be sitting in the long hand. And if the Q four times sits behind the A K J, it would seem that there is no way to pick up 4 heart winners. But the queen isn't sitting behind the A K J but before those cards, and so declarer can make the hand even if he goes for the drop in clubs, thus:
Win the opening spade lead. (Some played from the opposite side of the table on a strong, game-force 2 club opening bid, and it looks as though the a diamond J opening lead would queer declarer's chances unless he picks up the Q of clubs. East can ruff the third round of hearts and pick up a diamond winner.) Anyway, declarer plays the A, K of clubs, in that order, noting that he must lose a club, finesses the J of hearts, cashes the A of hearts, leads a low heart. If East ruffs, you sluff a diamond and now only need the K of hearts to throw another diamond. If East sluffs off, declarer ruffs and leads a club himself. That is because declarer now has only one entry to dummy and must sluff two diamonds and cannot afford to have his sluffing interrupted on the first sluff of a diamond.
Recapture the lead, go to the A of diamonds, and now the K of hearts will be used to sluff one diamond and draw the last of the opposition's hearts, with the 6 of hearts then used to sluff a second diamond.