Or we could change the rules of the game and see what happens when Monty opens the door we originally picked, but we're wearing blinders and can't see anything.

So in this game, there are 9 ways to play: 3 where we stick with our first pick, 6 where we switch our second pick.

By sticking with our first pick, we win 1/9 of the time, we lose 2/9 of the time.

By switching our second pick, we win 2/9 of the time, we lose 4/9 of the time.

First pick: we pick door 1 but the car was behind door 3

Second pick: we stick with door 1, because we can't see that we've already lost: Lose

Second pick: we switch to door 2, but it's not there: Lose

Second pick: we switch to door 3, and there it is: Win

First pick: we pick door 1 but the car was behind door 2

Second pick: we stick with door 1, because we can't see that we've already lost: Lose

Second pick: we switch to door 2, and there it is: Win

Second pick: we switch to door 3, but it's not there: Lose

First pick: we pick door 1 and there it is: but we can't see, so we don't know that we've potentially won

Second pick: we stick with door 1, because we're lucky: Win

Second pick: we switch to door 2, because we're unlucky: Lose

Second pick: we switch to door 3, because we're unlucky: Lose

This is much more entertaining for the audience, and much more crushing for us, when we seemingly should win, but decide to switch, and end up loosing.