[AnimalMuppet]

In the real world, you know by watching the show. Monte Hall always offers to switch, so that you know that you're in world A.

If it was the first time the show ever aired, you could be in a situation where you didn't know whether it was A or B. But in the problem as normally posed, you have time to watch the show for months to years, and you know how Monty behaves.

[Myto]

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.