The Empyrean Heights

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

Declarer took the opening lead with the A, cashed two top spades, sluffing two clubs and now ran diamonds, then the top hearts, then at trick 13, the 5 of hearts for all 13 tricks. West was holding, after ten tricks, the Q of spades, the J of hearts and the Q of clubs. Yikes! This one's almost too easy to discuss. I mean, declarer's locked in dummy when he goes there on his first diamond lead, which West can be certain of by round 3 of diamonds, long before he's put to any guess or even need to reason. The only way he could get off dummy would be to lead to the Q of hearts, and if he has that card, then he's on claim.

And if he doesn't have that card, the East has it, and West needn't worry -- unless the queen will fall in two leads. Then it becomes incumbent on West to save his hearts. The Q of spades is meaningless. If declarer is harboring the J, he can't use it, on a discard of the Q, because he has no access to it. If he has the highest club outside of West's hand, he can't use it, since he has no access to it.

This case is too easy to discuss further. A counterpart had the same problem of what to save, only the long diamonds were in the closed hand, and this defender has an entirely different calculus to pursue. Indeed, he must not save the same length as dummy in clubs, for declarer sluffs two on the top spades. And had he been watching, for declarer also sluffed two from the other hand on the long diamonds, he would have learned just soon enough to jettison his last club and save three hearts. At trick 10, on the lead of the 2 of diamonds, that defender's partner jettisoned his last club, allowing a sharp defender to note that the suit was splitting 4-triple-3 and thus declarer has no more and can have only hearts after diamonds are exhausted. [Remember, the closed hand is the North hand above, so the hand with the club spots plays second hand on the last diamond, the hand with the high clubs and 3 hearts plays fourth.]

That requires far more alertness than the first defender needed. And I think you might find it easier to count if you do so by distribution. Opening club lead, declarer immediately sluffing two clubs on dummy's spades. Well, now. Did declarer start with three also in the closed hand, the suit then splitting 4-3-3-3, or could he have four, the suit splitting 4-4-3-2? The defender counting cannot know when he has seen two sluffs from the closed hand and one from his partner. Either one could have that last club. But when his partner throws his last, East must know that the suit was originally 4-3-3-3 and declarer can have no more in the closed hand.

West's club discards were (after the lead of the 7), the 6 on his first opportunity, and then after sluffing two spades came the 9 at trick 10, before his partner had to play. West wasn't offering his partner much help. The 7 followed by the 6 tends to indicate a doubleton. Further, since he can't even beat dummy's 10, there's no reason to hang onto the 9 one second longer than he must and an early discard might have reached his partner's mind. Still, East had time. At trick 10, he held 3 hearts and the K of clubs, and his partner threw the last club East couldn't see, meaning East can discard the K of clubs with impunity and save 3 hearts.

Is there a contradiction here: the first defender must save the same number as dummy, but in the second case, East must not save the K of clubs with the 10 showing? Oh, I don't think so. First of all, nothing beats common sense, whatever maxims you've picked up. I've said this applies "by and large" when there are no other considerations. In the first case, declarer cannot possibly make use of any black honors he might be harboring. Only a heart trick remains to be decided, so you might as well save hearts. In the second case, with the long diamonds in the closed hand, that 10 of clubs could be a winner if East discards his top honors and declarer started with 4 clubs (improperly indicated by West's high-low play in clubs). And East wants go protect against the 10 of clubs until his partner's third discard should have or could have made it clear that declarer cannot have another club.

So the second layout has nothing to do with saving the same number as dummy, but, when you think about it, has a lot to do with saving the same number as the closed hand once you are satisfied that declarer has no access to dummy. Indeed, far from being a contradiction, declarer's lack of access to dummy has already been given as a reason for not saving according to what you see in dummy.