If the format of the game allows him to show the car to the player, how could his personality not enter into it? In every case where the player picks a goat-door, the host will be presented the option to either reveal the car or the goat. I mean, one can imagine various complicated scenarios in which the host might reveal the car exactly 50% of the time in such cases, but none seem like they can be reasonably arrived at.
it turns out that there is in fact no way that his personality could not enter into it, but that was not obvious to me until i did the simulation. even if he chose to reveal the car exactly 50% of the time in such cases, that would be a result of his personality, wouldn't it?