> One of the things that interests me about this paradox is that when you're left with just two doors, the odds of either of them being the one with the car is

> One of the things that interests me about this paradox is that when you're left with just two doors, the odds of either of them being the one with the car is 50%. Well, no, that's the point of this, it's not 50%. Before you pick there is a 1/3 chance of the car being behind any of the doors, so there is a 2/3 chance of it cumulatively being behind the other two. But there is only one car, so the set of doors you didn't pick must include at least one non-car. The host knows the location of the car so can always open a non-car door from this set. But still as a set they have a 2/3 chance of containing the car. By swapping you can effectively think of it as choosing both other doors. An easy way to get your head around this is increase the number of doors, say to 100. You pick 1 of those 100, the host opens 98 other doors, do you swap?