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Let's say you're declarer in four spades and West leads a heart. You win with the king and draw three rounds of trump. Since you have an inevitable heart loser, you must now try to avoid losing three club tricks.
If you play the ace and a low club -- hoping the suit divides 3-3 or that either opponent has the doubleton king -- you go down one against proper defense.
But if you play the clubs more carefully, you make the contract. After cashing the ace of clubs, you should continue with the queen rather than the deuce. This slight modification in the play yields a much more satisfying result. West's king and East's ten fall on the same trick, so you lose only two clubs instead of three.
It might be argued that playing the queen is right if you see all four hands, but that there is no justification for playing the queen if you see only two hands.
It is not difficult to refute this argument. Obviously, if the opposing clubs are divided 3-3, it makes no difference whether you lead the deuce or the queen.
But if the clubs are divided 4-2, the card you play will frequently make a difference. Since the player holding the doubleton will be dealt J-x or 10-x twice as often as K-x, it is clearly better to play the queen than the deuce.
Finding the correct percentage play of the queen is by no means a complicated mathematical proposition. It's simply plain common sense.
Tomorrow: It's a partnership game.