Keeping an eye on the count

Someone asked what the usefulness of count signaling is. One common use is when there's a long suit in dummy without external entries, like so:

Contract: 3 NT 
Lead:  Q

North

 8 3 2

 4 2

 K Q J 10 4

 7 6 5

West

 Q J 10 7

 K 10 7 3

 9 3 2

 J 10

East

 9 6

 Q 8 6 5

 A 7 5

 8 7 4 2

South

 A K 5 4

 A J 9

 8 6

 A K Q 9

South wins the spade lead in her hand. She has four club tricks, two spade tricks, and one heart trick off the top -- two tricks short of her contract. She leads a low diamond toward dummy. East has to decide whether to win the trick with his ace or not. If he wins the first diamond trick, South wins whatever card is returned and leads to dummy's four established diamond winners, making 5NT. If East holds up the ace until the third diamond trick, South wins two diamond tricks in dummy, enough to complete her 3NT contract. The way to defeat the contract is for East to let dummy win exactly one diamond trick, then take the second with the ace. How to figure that out? Count signaling.

When South leads the first diamond from dummy, West plays the 2. This is the start of a low-high count signal, indicating to East that West started with an odd number of diamonds. East does a little mental arithmetic. Dummy has five diamonds and East has three. The odd number in West's hand is obviously not 5, since that would leave declarer with zero diamonds. It's probably not a singleton either -- if it is, there's no defense against South taking her diamond tricks. So the assumption is that West started with exactly three diamonds, so declarer must have exactly two. If West holds up the ace until the second trick, declarer won't be able to get back to dummy's diamond winners, because there are no outside entries. Declarer is held to eight tricks, and the contract goes down -- all because of counting.