The assumption is that Monte will only reveal the one of the two unopened doors that has the goat behind it, as opposed to picking a door at random (which may be the car or may be the door the participant chose, which itself may or may not be the "car door").
The distinction is at which point Monte, assuming he has perfect knowledge, decides which door to reveal.
In the former, the chance to win is 2/3, in the other 1/2. However in any case, always (always meaning: in each condition, not in each repetition of the experiment, as this is irrelevant) switching is better than never switching, as there your chance to win is only 1/3.
How is it an "assumption" that Monte reveals a goat? Doesn't the question explicitly state that Monte opened one of the other two doors to reveal a goat?
Are there versions of the question where Monte doesn't reveal a goat behind his door or chooses the same door as you?
The distinction is at which point Monte, assuming he has perfect knowledge, decides which door to reveal.
In the former, the chance to win is 2/3, in the other 1/2. However in any case, always (always meaning: in each condition, not in each repetition of the experiment, as this is irrelevant) switching is better than never switching, as there your chance to win is only 1/3.