Monty Hall problem problem (idea)

Someone who does not make the assumptions that Monty Hall knows where the car is and that he will always open a door containing may instead assume that Monty always open a door entirely at random, and if that happens to be the one with the car, then you just lose immediately. In that case, there is no advantage to switching; 1/3 of the time you will have picked the right door, 1/3 of the time you will have picked the wrong door and Monty will open the other door which does not have the car, and 1/3 of the time Monty will reveal the car and you will not have any opportunity to switch doors. Furthermore, after Monty opens the door, in this case, the cases where Monty shows the car are now known to have not occurred, and the others are equally likely -- no advantage to switching.

This is how many people reach the "incorrect" answer that there is no advantage to switching, when the information that is supposed to be given about Monty's behavior is omitted from the problem. This isn't always an unstated assumption, and I seem to recall that in the problem's first appearance on rec.puzzles way back when, this information was included in the problem statement, but it is exactly the sort of thing that gets omitted often when this puzzle is retold.

The other problem with the Monty Hall problem, and this assumption in particular, is that the actual show Let's Make a Deal did not work like this. This was a game with no consistent rules, and Monty quite often, seemingly intentionally, did exactly the opposite of what you might have expected him to do or what he had done before in a similar situation.