User:Hydnjo/Many Doors problem

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In search of a new car, the player picks door 1. The game host then opens door 10 to reveal a goat, then opens door 9 to reveal a goat, then opens door 8 to reveal a goat, then opens door 7 to reveal a goat, then opens door 6 to reveal a goat, then opens door 5 to reveal a goat, then opens door 4 to reveal a goat, then opens door 3 to reveal a goat, and offers to let the player pick door 2 instead of door 1.

The Many Doors problem is a puzzle involving probability loosely based on the Wikipedia article Monty Hall problem which is loosely based on the American game show Let's Make a Deal. That name comes from the show's host, Monty Hall. A widely known statement of the Monty Hall problem is from Craig F. Whitaker of Columbia, Maryland in a letter to Marilyn vos Savant's September 9, 1990, column in Parade Magazine (as quoted by Bohl, Liberatore, and Nydick). The following is a parody which is loosely based on that statement so as to describe the Many Doors problem.

Suppose you're on a game show, and you're given the choice of ten doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens 8 other doors, say No. 3 through 10, which all have goats. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?