Game One: You are given a choice of three doors. You pick number one. The host opens one of the other two doors, having been given instructions that, if you pick the car, the host is to open one of the other doors, and if you pick a goat, the host opens the other door with a goat. Stalemate. It is a predetermined outcome.
Game Two: The prior game’s outcome stands. The new choice you have is do you keep door number one, or do you switch?
How do you have a 2/3 chance of winning if you switch?
In: 107
The way that helped me think about this was what if there were a million doors?
You pick on, and then the host opens 999,998 more leaving you with the one you picked, or one door from 999,999. Obviously you didn’t pick the right door out of the million, but in opening those other 999,998 doors the host knows exactly where the prize is and obviously avoids that. So of course you should switch.
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