[bztzt]

the ambiguity is that it's presented as something the host does in this particular instance, but the validity of the probability calculations depends on it being a protocol the host always follows (in particular, that the host will always reveal one of the goats not behind the contestant's first choice of doors).

[mcphage]

There is no "always follows". This is an event which will not be repeated in the history of the world. All there is is 3 doors: you pick one, the host opens another door which contains a goat, and offers you a choice. Why he picked the door that he chose is irrelevant. All that is relevant is that (a) it's not the door you chose, and (b) it contains a goat. You don't need anything beyond that to solve this problem. If you think you need something beyond that to solve the problem, you're not solving it correctly.

[PalmerEldritch]

"Why he picked the door that he chose is irrelevant" I disagree. If he picked the door at random and it just happened to contain a goat it's 50/50. If he picked the door because he was always going to pick that door if it contained a goat then it's 50/50