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The Monty Hall problem is a brain teaser, in the form of a probability puzzle (Gruber, Krauss and others), loosely based on the American television game show ''Let's Make a Deal'' and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the ''American Statistician'' in 1975 , . It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in ''Parade'' magazine in 1990 : Vos Savant's response was that the contestant should switch to the other door . Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their choice have only a 1/3 chance. The given probabilities depend on specific assumptions about how the host and contestant choose their doors. A key insight is that, under these standard conditions, there is more information about doors 2 and 3 that was not available at the beginning of the game, when the door 1 was chosen by the player. Other possible behaviors than the one described can reveal different additional information, or none at all, and yield different probabilities. Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in ''Parade'', approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong . Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy . Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation confirming the predicted result (Vazsonyi 1999). The problem is a paradox of the ''veridical'' type, because the correct result (you should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true. The Monty Hall problem is mathematically closely related to the earlier Three Prisoners problem and to the much older Bertrand's box paradox. ==The paradox== Steve Selvin wrote a letter to the ''American Statistician'' in 1975 describing a problem loosely based on the game show ''Let's Make a Deal'', , dubbing it the "Monty Hall problem" in a subsequent letter . The problem is mathematically equivalent to the Three Prisoners Problem described in Martin Gardner's "Mathematical Games" column in ''Scientific American'' in 1959 (Gardner 1959a) and the Three Shells Problem described in Gardner's book "Aha Gotcha" . The same problem was restated in a 1990 letter by Craig Whitaker to Marilyn vos Savant's "Ask Marilyn" column in ''Parade '': 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Monty Hall problem」の詳細全文を読む スポンサード リンク
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