Mickey Mouse said, "Arithmetic is being able to count up to 20 without taking off your shoes."

Bridge is being able to count up to 13 without taking off one shoe.

To be honest, it is rare that you need to count a player's full hand distribution. But sometimes it is important. South benefited from a misdefense in this deal.

How should the defense have gone against six spades after West led his fourth-highest club?

The bidding was modern. North, rightly adding one point for his good five-card suit, deemed his hand too strong for one no-trump. South overbid slightly with three spades, which was a game-force. North control-bid four hearts to show a strong hand for spades, then used two doses of Roman Key Card Blackwood to learn that his partner had the spade ace or king (five clubs) and the spade queen and diamond king (six diamonds).

South won the first trick with his club queen and played a spade to dummy's jack. East, based on his partner's nonheart lead, should have taken the trick and given his partner a heart ruff, but he ducked, took the second spade and exited with a diamond.

Now South did well. He won with dummy's ace, drew the missing trump, took the heart ace and played a diamond to his king. What had he learned? That East had started with three spades, seven hearts, two diamonds and one club. So declarer played a club to dummy's nine to gain 12 tricks: four spades, one heart, two diamonds and five clubs.

(China Daily 08/26/2017 page20)