Bridge Game

The Principle of restricted choice is used in bridge to guide a player (usually the declarer) into finding the best line of play in certain situations. It is closely tied to the Monty Hall problem.

The principle can be expressed in several different ways; one of them is:

When a defender freely plays an important card (over declarer's lead), assume that it had to be played rather than it was result of a particular choice; adjust the subsequent play accordingly.

In other words, if an opponent unprovoked plays a honor card (e.g. a king) on declarer's or dummy's lead, it should be assumed that he had to play it (i.e. it was a singleton) rather than it was played from a combination of equal-rank cards (e.g. king-queen). With KQ, he could select either king or queen, but with bare king he had no choice. That makes singleton king twice as possible as bare KQ, so it should be assumed that it was singleton.

Example

Consider the situation as in the diagram (with "x" denoting insignificant cards with a small face value).

South leads a small card to dummy's (North's) Jack, but East wins with the King. Later in the hand, South leads a small card again, and West plays low. In the absence of other information, is it better to play the Ace in an attempt to crush East's Queen, or to take another finesse by playing the ten, playing West for three cards? The Principle of Restricted Choice explains that finessing is roughly twice as likely.

The initial possibilities were (ignoring 4-0 breaks):