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 easiest way to change your intuition for the game is to imagine there are 100 doors, and after you pick one, the host closes 98 others. Seems pretty obvious you should always switch now, yes?
Staying only wins if you guessed right on your first guess which is 1/3 chance. Switching always wins if you guessed wrong on your first guess, which is a 2/3 chance.
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