Page "Principle of restricted choice" Paragraph 0

In contract bridge, the principle of restricted choice states that play of a particular card decreases the probability its player holds any equivalent card.

For example, South leads a low spade, West plays a low one, North plays the queen, East wins with the king.

The ace and king are equivalent cards ; East's play of the king decreases the probability East holds the ace – and increases the probability West holds the ace.

The principle helps other players infer the locations of unobserved equivalent cards such as that spade ace after observing the king.

The increase or decrease in probability is an example of Bayesian updating as evidence accumulates and particular applications of restricted choice are similar to the Monty Hall problem.