[mjburgess]

I agree. I think a lot of these probability puzzles end up being "illusions of emphasis", ie., that we fail to grasp the problem because how components of it are expressed in language.

When the host opens the door and why need to be repeated several times and with lots of emphasis before asking the question. These ordinarily minor details are extraordinarily relevant, and the language used should express that.

[Rerarom]

Yes, because if the problem was expressed purely formally from the start, there could not possibly be any controversy. The appeal of Monty Hall is precisely this interplay of natural and formal language.

[daveFNbuck]

People aren't generally very good at probability. Plenty of people get it wrong despite understanding the puzzle correctly.