this post was submitted on 03 May 2025
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Every time I see this I spend 10 minutes reading the solution explanation in detail and still end up not gaining any intuitive insights. I'm sure the "switch" probability is better but I always have more questions.
If the host knows where the car is and picks a door that doesn't have the car, I understand that that is technically gained information compared to the starting state in which the initial door was chosen, but why does that information matter? As a counterfactual, why doesn't it remain just as theoretically possible that the unpicked/switch-to door was the initial chosen switch-from door and therefore there is an equal likelihood that both doors contain the car?
That's what keeps stumping me.