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
Here’s a slightly different way to look at it: After you pick your first door, *Monty is compelled to show you a goat*. If your first door was a goat (2/3) you win by switching. If your first door was a prize (1/3) you lose by switching.
When Marilyn Vos Savant started the big controversy on this years ago, she used language that made it sound as though Monty *just happens* to show you a goat, like it was some sort of random act on his part. Not so. He ALWAYS has to show you a goat. Two times out of three, when your first pick is a goat, Monty guarantees a win by showing you the other one.
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