Monty Hall

by Douglas Zare
7 June 2010

Douglas Zare

Probability is important in backgammon. We deal make decisions under risk, and we have to interpret noisy evidence, such as playing out a position a single time when it would take a rollout with thousands of trials to be conclusive.

One illustration that probability is counterintuitive is the Monty Hall puzzle.

The overwhelming majority of people who have encountered it have an incomplete understanding. First, many (perhaps most) come up with the wrong answer. Second, even those who find the right answer may not have the right reasons for choosing the right answer. This is very common. The result is that many statements of the Monty Hall problem are incomplete, and many supposed solutions are incomplete and unconvincing. Many of the people who stick to the wrong answer may do so because they recognize errors in explanations for the correct answer.

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