Puzzles

A warden's harmless-seeming answer secretly changes a prisoner's odds

Three prisoners, A, B and C, are told one of them — chosen at random — will be pardoned. Prisoner A, knowing the warden can't reveal his own fate, asks instead to be told the name of one of the other two who will be executed. The warden, who knows the outcome, names B. Has A's chance of being the pardoned one now risen from 1/3 to 1/2?

Reveal the answer

No — A's odds are still exactly 1/3; it's C whose odds have jumped, to 2/3. Naming B gave A no information about himself, only about B and C, and the way the warden had to break a tie (if A were the pardoned one, he could have named either B or C) skews the update entirely onto C. Martin Gardner posed this in his Scientific American 'Mathematical Games' column in 1959, more than 30 years before the mathematically identical Monty Hall problem became famous.

Martin Gardner, Mathematical Games — Scientific American, 1959

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