[Sohcahtoa82]

Your proposal is changing the scenario, though.

In the original problem, Monty always opens a door to reveal a goat. This strongly implies that he knows which doors have goats.

Your alternative is different. If the doors opened are truly selected randomly, then the odds are high that he would reveal a car, especially in the 1000-door version. What are the odds that Monty could choose 998 doors randomly out of 1000 and NOT pick the one with the car?

If Monty doesn't know where the car is, then you're arguing with a completely different version of the game that could result in him opening the door with the car, so the strategy is going to be different.

[kmm]

Changing the scenario is the exactly the point of why I am unsure increasing the number of doors gives true intuition. In the original problem with the original scenario, people intuitively think switching doesn't matter, when it provably does. With 1000 doors and the Monty Fall scenario, again the intuition is wrong. So are we gaining true intuition for the Monty Hall scenario by expanding the setup, or is it just some subconscious Bayesian thinking accidentally steering us toward the right answer.