this is exactly what tripped me up when I first heard the problem and it took me a long time to understand the explanation because I didn't understand that Monty always opened the door that did not have the car behind it.
But it’s from a game show. Like, an actual show. 1/3 of the time they can’t just stop filming and say "whoops let’s pretend that didn’t happen." That interpretation of the problem makes no sense whatsoever.
But that means that something knows which door was the winning one. Either Monty knew which one it was, or whatever mysterious Agent is sampling from all the possible outcomes knew (because the Agent only sampled the ones where Monty happened to open a non-winning door). Either way, you're given the choice between having the 1 door you initially chose, or both of the other doors.
> Either way, you're given the choice between having the 1 door you initially chose, or both of the other doors.
i initially thought this too, but in both cases you're gonna see 2/3 doors. the thing that makes the difference is when he has the car (2/3 of the time), he has to tell you where it is. so the choice becomes between your unknown door and his 2/3 selectively chosen car door.
