> because it comes from a game show where he always reveals one wrong door.

Nope!

> Was Mr. Hall cheating? Not according to the rules of the show, because he did have the option of not offering the switch, and he usually did not offer it.

Emphasis added.

https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-do...

Ah, but probability is all about hypothetical instances, and how the host makes his decisions—or if he’s allowed to make a decision at all—is a key consideration in the calculation of the probability. If we don’t know how the host decides whether or not to offer a switch then we can’t calculate a probability and can’t decide which choice is better.

Yes, I am discussing a different problem, and I don't think the original problem formulation gives enough information to distinguish between the 2 problems.

The answer can add assumptions, which is fine. I'm not passing judgement on Marilyn vos Savant. I do object to claims that the problem statement is sufficient to have a single answer, and based on that, I'd object to claims that somebody in that situation would be wrong not to switch doors. I would object on exactly the same grounds to anyone who tells you "you're wrong, there's a 50% chance of getting a car" (I might object further, on the grounds that the most obvious interpretation which gives that answer is inconsistent with this form of the problem statement).