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
If they *randomly* chose one of the other doors to show you, then the odds would be 50/50. But also, the randomly chosen door has 1/3 odds of having the car. Since they *intentionally* show a goat, then that changes the odds.
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