Sorry, I wasn't at all clear. The 'statement of the obvious' to which I was refering was that it would be right to switch if he'd originally chosen the goat and wrong to switch if he had initially chosen the car!So it tells him the probability of it being better to swap, and the probability of it not being better, and one of those numbers is larger than the other, and that doesn't tell him whether it is better to swap or not swap? Not sure I see that....
The probabilities you mention are where all the hair starts being pulled out! They were, indeed, true at the time the initial choice was made, but that was at a time when there were three 'unknowns' to choose between. Once one 'goat door' has been taken out of the equation, it is very hard (even if one should!) to get one's head away from the thought that there are now just two doors, one with a car and the other with a goat, and that there 'must' (famous last words!) be an equal probability of the car being behind either.
You are, as you know, right in your conclusion/answer, but it isn't anything like as obvious as you are suggesting. Can you, for example, answer this .... once one door has been revealed to have a goat behind it, why does the remaining situation differ from one which would have existed if that door never existed, and one simply had chosen between two doors, one with a car and the other with a goat?
I had been hoping to avoid getting into 'the discussion', but (I suppose inevitably) it seems to have happened!
Kind Regards, John