The problem with 'The Monty Hall Problem' was Monty Hall

[DukeTrout]

@anon21100188

First of all, the opportunity to switch is what the MHP is all about: how switching greatly increases one’s probability of guessing correctly.

Second, even if the opportunity to switch is denied, the fact remains that the original guess has a 1/3 probability of being correct. It doesn’t become 50/50 if other doors are opened before the winning option or not.

It took me a while, but I’m getting it, and where I went wrong. I was just jumping to the (mathematical) assumption that the prize re-randomizes when MH opens one door. Which they hypothetically could have done in the show, but it would be, I assume, unethical. Without redistribution of the prize, the denominator stays the same as the original randomization.

Thanks!