> The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows where the car is and this knowledge is always used perfectly. If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious.
The associated line of reasoning resolved the paradox for me. If I stick with my original choice, it is as if I ignored the new information. If I switch the choice, I react to the new information.
The extreme of this is to pick among countably infinite doors, having the presenter open countably infinite doors and leaving just yours and another closed. Who could reasonable suggest that the chance is still 50/50, assuming you don't flip a coin and base your choice on that?