re: Marilyn vos Savant and the history of the Montel Hall question

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no, a million cards flipped upside down. one of them is a million dollar grand prize. you can pick any card, then 999,998 incorrect cards are flipped over. you're given the choice to stay with your original 1-in-a-million chance or switch. remember, you're all jason's got, and he's depending on you.

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You switch again. You have a 99.9999% chance of winning if you switch.

Here is the formulation for any scenario from Wikipedia:

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D. L. Ferguson (1975 in a letter to Selvin cited in (Selvin 1975b)) suggests an N-door generalization of the original problem in which the host opens p losing doors and then offers the player the opportunity to switch; in this variant switching wins with probability (N-1)/[N(N-p-1)]. If the host opens even a single door, the player is better off switching, but, if the host opens only one door, the advantage approaches zero as N grows large (Granberg 1996:188). At the other extreme, if the host opens all but one losing door the advantage increases as N grows large (the probability of winning by switching approaches 1 as N grows very large)

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