[hulium]

If the the door contains a car, then it doesn't matter whether you switch or not. If it is a goat you get the problem as intended.

You still have the intended problem as a subproblem, so this is just a distraction and not a serious objection.

[tga_d]

If a goat was revealed randomly instead of intentionally, there is no advantage to switching. See the "Monty Fall Problem" in this paper already linked elsewhere in the discussion: https://web.archive.org/web/20230706235720/https://probabili...

To use the 100 door extension some people find helpful: If Monty always reveals the 98 doors that don't contain goats, then 99% of the time (every time you picked a non-car door), the other door will have the car. If Monty is opening a random set of 98 doors, then 98% of the time Monty will reveal the car, 1% of the time you'll have picked the car on the first guess, and 1% of the time the car is in the other door. When you're in those 2% of cases where no car is revealed, you have a 50/50 shot of being in either of the 1% states where that happens.