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You don't have to be a great mathematician to be a good declarer (or defender). All you need is the ability to count to 13.
Consider this deal where West leads the Q-J of hearts, which South allows to hold, and then shifts to a low spade. It is certainly reasonable for declarer to conclude at this stage that West started with exactly two hearts.
South wins East's jack of spades with the ace and plays a diamond to the queen. East takes the ace and returns a heart to declarer's ace, on which West discards a spade.
When South next leads a diamond to the king, West discards a club. Declarer cannot actually see West's hand at this point, but it is nonetheless clear that West, who has thus far shown up with just two hearts and one diamond, must have started with five spades and five clubs, judging from his two discards.
South confirms West's 5-2-1-5 distribution by cashing the K-Q of spades, on which East shows out. Declarer's proper continuation is now clear-cut. He has an end play in the making that guarantees four club tricks and the contract.
South cashes dummy's king of clubs and then leads the five of spades, forcing West to win with the ten. West's last three cards are the J-9-8 of clubs, and he must return one to South's A-Q-10, putting an end to the proceedings.
It is true that declarer had to employ some basic arithmetic as the play progressed, but at no point did his calculations get any higher than the number 13. Counting out a hand can be extremely profitable if a player is willing to go through the rigamarole of adding and/or subtracting simple whole numbers. The only drawback is that it takes all the guesswork out of the game!
Tomorrow: One card points the way.
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