I've never watched the show, but I have read that that is not the case; sometimes he gave the option to switch, and sometimes not. Even if that were the case, it is not stated in the problem and therefore you cannot assume he behaves like he might in the real world. Also even if he had allowed the switch every previous time, it still does not logically mean that he does that the one time you are playing.

And once more, I'm talking about the problem as given, not some other problem. It is a self contained math / logic problem.