Oh dear Rick, we are back your misunderstanding of what probability means.  I am not sure if we are allowed to discus this any more, perhaps it is OK on this page.

Richard confirms above that there are two interpretations of probability, Bayesian and frequentist.  Although they both should give the same answer to any exact question it is very confusing to flip interpretation in the middle of an argument.  I am happy to discuss the MHP using either model but let us start with the Bayesian perspective first.

To a Bayesian, probability is a state of knowledge.  That is the definition of what Bayesian probability means.  In the Bayesian model, what is not known does not exist.  That is not something  that I have just made up, I am sure Richard will confirm it or you can confirm it using WP or any good text book.  So, if the player does not know where the car is placed, or the host's door opening strategy, the probability of winning by switching is exactly 2/3.  It may be that the car is always placed behind door 2 and the host always opens door 3 but, if we do not know that, it makes no difference to our (Bayesian) probability calculation, which depends by definition only on the information that we have, .  The concept of average probability makes no sense, there is just 'the probability' which is based only on our state of knowledge.