Partner opens 1NT (12-14). Everyone passes, and RHO leads the ♥J. If you have bridge-playing software that can read the PBN file linked to above, you might want to try your hand at declaring 1NT yourself before reading on.
If diamonds are 4-4, I can afford to lose two club tricks. If they are 5-3, I need to pick up the clubs or hope they don't find a diamond shift. The best play in clubs is to lead through the hand more likely to have a singleton in case that singleton happens to be the ace.
Which defender is more likely to have a singleton club? A singleton in either hand would make entering the auction more attractive. But West needs a better hand to bid in direct seat than East needs to balance. So East's silence is louder. If anyone holds a singleton, it is probably West.
If the opponents played standard leads, I might have reason to play the ♥Q from dummy to disguise the fact that I have ♥AK. But the opponents play that the lead of the jack denies a higher honor, so East already knows I have those cards. Since I want to attack clubs by leading toward the dummy, it makes sense to win this trick in my hand.
I play low from dummy, East plays the ♥9 (upside-down attitude), and I win with the ♥K. I play the ♣4 (I can't afford the ♣7. If West shows out on this trick, I will need that card.)--♣8--♣Q--♣A. I expect a diamond shift. Surprisingly, East returns the ♥3--♥6--♥4--♥Q. What a strange play! East knows I have the ♥A. If clubs are running, I have seven tricks. How can he not try to cash six more tricks before letting me in? One thing I can be sure of: East does not have five diamonds. If he did, he would switch to a diamond in an attempt to cash five diamonds and the ♠A.
The ♥2 is still out. East's ♥3 could be high from ♥32 doubleton. Or it could be his only heart, in which case West is concealing the ♥2, either for deceptive purposes or simply because he is giving present count. Jack, however, is not big on present count, nor is he big on deception. So I suspect East has the ♥2 and hearts are 4-3.
I lead the ♣2, and East plays the ♣5. The moment of truth. My play doesn't matter if diamonds are 4-4, so I must assume they are five-three. I've already concluded that it's impossible for East to have five diamonds. So I must assume West does.
Would West really lead a four-card heart suit holding five diamonds? Probably not if we were in three notrump. But in 1NT, where West expects the defense to have more entries, he might well avoid leading a five-card suit that might more profitably be attacked by his partner. Besides, if he doesn't have five diamonds, I have no problem. So I might as well assume he does.
Is West more likely to be 2-4-5-2 or 3-4-5-1? A priori, 3-4-5-1 is more likely (since a 5-2 spade split is less likely than a 3-1 club split). On top of that, East's heart continuation suggests he has some hope that clubs aren't running. ♣AJx would offer more hope than ace doubleton. And, if that's not enough, there's some chance I could survive a finesse even if it loses. With something like
Plus... it's free!