>>15006307

This was the only one that actually worked intuitively, with no thinking required, on me:

You have to realise that it's not one game, it's two small games played one after another. The first game is just "pick a door", and obviously there your chances are 1/3. The second game, "stay or switch", has two possibilities:

A) you think your 1/3 guess in the first game was right and stay, or

B) you decide that you were probably wrong, and switch.

These, A and B, are the only possible answers. A has a win-rate of 1/3, obviously, and so B *must* have a win-rate of 2/3.

That's all it is. No prognosticating about what Monty knows, no "what if there were 100 doors" nonsense, you just need to realise it boils down to betting on if a 1/3 guess was right or not.