this post was submitted on 07 Dec 2023
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With 100 doors switching should give you a 99% win rate.
You're essentially concentrating the entire thing into this one vs not this one, and when you initially chose there was a 99% chance it was not this one.
After Monty opens all the other doors, the odds that the right answer is not this one is still 99% except that now the entirety of not this one is represented by that single other door. The Grand Prize has nowhere else to be, and the odds that you picked it first is still only 1%.
So, to bring it back down, with three doors, the odds that the right answer is not this one 66%, and we end up exactly where we expected to be.