::::Thanks for that answer, during which I was already typing. So firstly, to respond specifically to your last-but-one post above: 
 I mean the probability of choosing a goat or the car from the contestant's perspective. 
 I am distinguishing deliberately revealing a goat from other host behaviors because the contestant can infer the former (by the information that he knows what's behind the doors being superfluous if he is random) while the latter cannot be inferred from the information given. 
 Randomly revealing a goat would look no different, but the contestant has the information to infer it is not random on this occasion. 
 The Bayesian may calculate (not guess) 2/3, as the set of all possible unstated hindering variant behaviors and the set of helpful ones are equal in likelihood and opposite in value, thus neutral to the solution. Although I think the absence of any positive information means the assumption of 'no motive' is a safe one. 
 The frequentist answering the MHP question (ie 'In the circumstances stated in this scenario, is it to your advantage to switch?') would only count those games where the MHP circumstances apply, and their solution would approach 2/3.  
 As to the specific sources, making the same conditions is not the same as using the word 'always' - the precise conditions might only occur once in a series of similar games, or even once in all time, with the result on that occasion still 2/3. 
 I should emphasise that while variant scenarios may occur without affecting the MHP when it occurs, if variant host behavior can be discerned by the contestant a game meeting all the other conditions cannot be the MHP; as vos Savant put it "Anything else is a different question". 
 Regarding your most recent post, I get basic conditional probability though am a novice in math and stats. The first time the MHP ever occurred the probability was 2/3. If it never occurred again, it was still 2/3. Now every time those conditions come together it's 2/3. If the host revealed the car on yesterday's show but you don't know why, it's 2/3 if the MHP comes together today. I am not disagreeing with the assumptions, or that they 'must' accompany the MHP, just with the word 'always'.