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
Something that really emphasizes the way the math works is to imagine you have 100 doors instead of 3.
Say you pick door 23. The host then opens all the doors the car isn’t behind, going one by one. 1, 2, 3, 4, on and on, all empty. He skips your door then keeps opening empty doors. 24, 25, 26, on and on. But then he skips door 72 and finishes opening doors. Would you switch to door 72? Obviously.
The same logic applies, albeit much less obviously, to 3 doors.
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