“it’s much easier to think about with higher numbers. ie., 1000 doors; your odds of picking the winner is 1:1000. the odds of the car being behind any one of the remaining doors is 999:1000. eliminating all of the other incorrect doors means that the chance of the car being in the door you didn’t pick is 999:1000.”
In this case, your odds BEFORE the game starts is pretty good; 999/1000. BUT once the 998 doors are open, the odds of the first choice door or the switch choice door holding the car are the same: 1/1000 of the original number, or 1/2 of the remaining unknown doors. Switching makes no difference. Knowledge of what was behind the 998 open doors does not create any knowledge of what is behind the remaining 2 closed doors.
I reserve the right to be wrong, given that some really smart guys see it the other way, but it seems pretty simple. There’s no difference between the remaining 2 closed doors.
