RE: Would you switch?

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(Edited)

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Your scenario cannot happen because the host is not allowed to open the chosen door (otherwise 'stay or switch' doesn't make sense). So if the contestant picks a penny door, the host is forced to open the other penny door.

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Sure. In a game show that methodology cannot be applied. The host cannot open a door using chance in case they pick the winner.

But outside of a game show, say as a puzzle in a book, the idea holds that:

  • If you have chosen a door
  • And an alternative door is opened without success
  • Then the probabilities of whether you should stick or switch depend on whether the alternative door was opened through knowledge or chance.

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Oh, I see what you are saying now. Your setup is a one-time scenario, and the contestant doesn't know the rules of the host. (e.g. the host rule was to flip the other doors randomly, and it happened to get lucky and not reveal the 1M, or the host in this case just opened the penny door and tells the contestant that it was flipped randomly).

But I think the wording of the original post is clear that "one of the doors with a penny behind it will be opened", and that implies it cannot be done by chance.

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