queen – for the queen from that East player almost denies the king. Mathematical theory The principle of restricted choice is an application of Bayes' theorem on conditional probability. In the following: represents the condition that the King is played by East in the first trick; represents the condition that East holds KQ and; represents the condition that East holds K. The two conditions are as follows: We assume that when East holds KQ, he plays each 50% of the time and when he holds the K alone, he must play the K. This is represented by the following: Further, based on the play to trick 1, only two of the original 16 (i.e., a priori) possible holdings shown in Table 1 above remain available for East, each equally possible. Solving, we find (posteriori) that... In conclusion, we can say that "after East has played the K on the first round, the probability that East started with the singleton K is twice as probable as that he started with the KQ." The first two equations are Bayes' theorem, the rest is simple algebra. Increases and decreases in the probabilities of original lies of the opposing cards, as the play of the hand proceeds, are examples of Bayesian updating as evidence accumulates. See also Monty Hall problem Notes Further reading The article on Restricted Choice was originated by Jeff Rubens in the first Encyclopedia (1964 edition). In it and subsequent editions (e.g. on page 381 of the 6th edition), Rubens states that Reese in his book Master Play "unified" the "underlying principles ... first discussed by Alan Truscott in the Contract Bridge Journal"; he does not give a date for the Truscott article. Republished in the USA as External links "Monty Hall problem and the principle of restricted choice" "Bridge paradoxes" by Richard Pavlicek Contract bridge card play Contract bridge probabilities