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A comment on Ask HN: What is a science fact that blew your mind when you learned it?. Parent comment
- If you happen to choose a door with a goat (⅔ of the time), the host has to choose a goat door, leaving "switch" a guaranteed win
- If you happen choose the door with the car (⅓ of the time), the host opens a random goat door and you have 50/50 between staying and switching
So always switching is the correct move - if you do that you'll win the ⅔ of the time (every time you open a goat door).
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- If you happen to choose a door with a goat (⅔ of the time), the host has to choose a goat door, leaving "switch" a guaranteed win
- If you happen choose the door with the car (⅓ of the time), the host opens a random goat door and you have 50/50 between staying and switching
So always switching is the correct move - if you do that you'll win the ⅔ of the time (every time you open a goat door).