This might be a small difference, but is this an english parsing or reality parsing issue? I mean, shouldn't these questions come up as you're mentally interro

This might be a small difference, but is this an english parsing or reality parsing issue? I mean, shouldn't these questions come up as you're mentally interrogating the scenario, and trying to win the car? What happens if the host opens a car door, do I win? If the host opens doors randomly, I have a 2/3 chance of winning anyway. But, I didn't have enough information to know that when I picked a door first. By the time I do, I'm already back to 50-50 odds. I don't think people make either 2/3 game their mental model of the game. IDK about non-mathematicians, but I taught a parlour-games-ish parent day class at a high school once. We solved this problem until the kids got it. Then they had to explain it to other kids. My hint was emphasising "every week he shows a goat." Then basically this program, "playing" over and over on blackboard and recording results. Either way, it takes effort before people think of the entire game (including the 2nd choice) as a single game mechanic. Almost everyone gets it if you make them play the host. Maybe mathematicians are less prone to suspicion... Kids and adult non-mathematicians usually suspect the host of being up to something, so they are animating him in their mental model. Anyway, I think there's something interesting about this problem, and how people have difficulty thinking about it. I wonder if the same mechanic, but with a differently decorated story would be easier for people? A robot host, for instance.