[justsee]

This seems the most interesting aspect of the problem:

"However, the probability of winning by always switching is a logically distinct concept from the probability of winning by switching given that the player has picked door 1 and the host has opened door 3." [1]

[1] https://en.wikipedia.org/wiki/Monty_Hall_problem#Criticism_o...

[Dylan16807]

Probability of an outcome always depends on what pool you're sampling from.

People pretty much always understand what the options are, but still get the analysis wrong. That is what I find interesting. Not the idea that there's some secret mechanism at play that alters the odds of a specific case. Even in that wonky "open the door on the right when possible" world, a contestant that always switches will still win 2/3 of the time.