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The one where Monty trips over a cord and opens a random door seems wrong to me. According to the explanation Monty doesn't give you additional information by a
by sfn42 2y ago
The one where Monty trips over a cord and opens a random door seems wrong to me. According to the explanation Monty doesn't give you additional information by accidentally revealing a goat, but it seems to me he gives exactly the same amount of information as he would by intentionally revealing a goat.
And the reasoning remains the same - when you pick a door you have 1/3 chance to pick the car, meaning the two other doors have a 2/3 chance to contain it. When he reveals a goat, my door is still 1/3 and the other one is still 2/3, so I should switch just like when he intentionally reveals the goat.
- weepinbell 2y agoI believe the origin is here and explains it in a lot of detail: https://probability.ca/jeff/writing/montyfall.pdf 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.