[moosinho]

I wouldn't say that's the core of the paradox. The thing is that people don't have a good understanding what probability is. We think that when we choose a gate at the beginning, with a chance of winning being 1/3 it means that the universe "rolls" a dice and decides whether we win or not. It is then very confusing to realize that someone else, just by revealing the content of one of the other gates - after our decision has been made - can somehow make the universe roll a different dice with 2/3 odds.

The paradox disappears when you think about probability as a tool for reasoning from incomplete information, not as anything to do with "physical" property of the system under investigation. It then makes perfect sense that after receiving new information from the host we should reassign our probabilities.