I think the biggest mind-blow with this paradox is that there seems to be nothing "special" about the other door when you switch. How is there something unique about that door that gives it better odds than the first door? It's special just because it's the one you didn't choose the first time? I find that quite weird. And yet the mathematics say it must be so.
An even stranger thing is if a new player (who has not observe anything) joins in when there are only 2 doors left, all he needs to do is to bet that the first player is a loser and he gets an edge...(turns probability from 1/2 to 2/3)
There are 2 goats and 1 car. So you can pick either of 2 goats behind door #1 wrong ( 2/3 ) and still win the car by switching ( 2/3 * 1/2). If you don't switch you have to pick car in your first choice correctly (1/3) to win (1/3 * 1/2).