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 can not 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 can not 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