Monty Hell problem

:A different article treats the Monty Hall problem.

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The Monty Hell problem is a paradox in probability theory involving infinite sequences of actions. As described in a post in the usenet group rec.puzzles, the problem consists of choosing between two alternative strategies for banking your money while spending an eternity confined in Hell. The assumptions of the problem are that each day you are paid $10 in $1 bills, but must turn over $1 each day to the Devil to pay for the heat. You are not allowed to handle your money yourself, but instead must choose one of two bankers:

Related Topics:
Paradox - Probability - Usenet - Hell - Devil

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• Monty, who puts each day's bills in a large sack, then chooses one of the bills from the sack uniformly at random (including bills from previous days) to give to the Devil.
• Marilyn, who carefully removes one bill from the stack of ten bills to give to the Devil, and then places the remaining nine bills in her sack.

The goal is to maximize your wealth at the end of your eternal confinement, which occurs on a hypothetical day ω (see Transfinite number), which occurs after all finitely-numbered days.

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(The problem is sometimes stated such that Marilyn removes nine bills and only puts one in the sack. Here, for simplicity, they remove the same amount of money daily.)

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Monty Hell problem: The paradox ►