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weepinbell | 11 months ago

I believe the origin is here and explains it in a lot of detail: https://probability.ca/jeff/writing/montyfall.pdf

I should add the credit line, looks like I left it off for that one, though I think the general concept is pretty common.

One possible intuition is that when Monty opens a goat door in the original problem, the fact that he didn't open the other non-chosen door gives evidence that that door has a car (because it's more likely he doesn't open if it does have a car than if it has a goat).

In the "Monty Fall" variant, it's equally likely that he opens it whether it has a car or not. So the fact that it wasn't opened doesn't give you additional evidence for what's inside it.

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