A thin slam

This thin slam from an ARBC duplicate defeated many declarers (in fact all of them). How would you try to take 12 tricks on the jack of spades lead to your king?

Count up your top tricks outside trumps: you have five — ace-king of spades and ace-king-queen of hearts. If hearts split 3-3, you will have an easy ride, for you’ll need only five trump tricks — that’s one diamond ruff. However, if hearts do not split 3-3, you’ll need six trump tricks — a third diamond ruff is impossible in practice — plus some fancy footwork in the endgame.

It has to be right to lose a diamond at trick two, voiding the dummy preparatory to some ruffs. The defence wins and leads another spade (as good as anything).

Winning the ace of spades, you ruff a second diamond with the king of clubs (note). You lead a low club to the ten and ruff a third diamond with the ace of clubs (East discarding — a spade). You return to hand by leading dummy’s last club to your queen-jack, drawing the opposing clubs, and we have reached this ending:

Needing the rest of the tricks, you may hope for a 3-3 heart split. In fact, though, you know they are not 3-3 — for East has revealed just two diamonds and two clubs. If he had three hearts, then he had six spades — impossible as West has shown up with two spades.

Nil desperandum. Lead your last club, and what can East discard? A heart gives dummy a fourth heart trick; a spade promotes declarer’s remaining spade.

Twelve tricks and slam made. Only a heart lead, then a heart continuation (which has to come from West, so East has to duck a diamond from dummy), defeats the slam.