The best part about the monty hall problem is that every description I have seen of it has always been entirely incorrect.
Changing your choice makes absolutely no difference.
Now, if the problem description had involved revealing a door that isn't the prize, rather than revealing a door that wasn't choosen, the "solution" would be correct. But that is never the case.
Interestingly enough, no matter the description, I have also never seen the prize-door be revealed by the theoretical game-host. Which is ludicrously improbable and I would almost argue dream-luck levels indication of 'cheating' where the example doesn't actually follow it's own description, and reveal a random un-choosen door.