"Eliezer S. Yudkowsky" wrote:
> For example, suppose that you're on a game show called "ExtroQuiz" and
> there are three doors: A, B, and C. One door has a prize behind it. You
> pick door C. The game show host opens up door A, and shows you that it's
> empty. What is the probability that the prize is behind door B? Answer:
> 0%. Why? Because the game show host *knows* the standard answer to this
> riddle, *knows* that most Extropians will switch to B, and he opens A *if
> and only if* the prize is actually behind C.
Another way to illustrate why it is best to switch doors after Monte
opens one is by restating the game thus: Monte offers you one of the
three doors, but before you choose, he writes a letter on a card and
places it face down. This is the letter of a door that he knows has a
goat behind it. He says that after you choose a door, which might be
the one he wrote, he will reveal the door written on the card. That
illustration may help some to understand why its best to switch, assuming
one prize and two zonks.
Eliezer's contention is incorrect methinks. If you choose C and it is a
zonk, Monte must open A, for he knows B is the prize. If you choose
C and it has the prize, Monte can open either A or B, and then you
switch and get zonked. So assuming Mr. Hall wishes to zonk you,
he can do so only if you originally chose the prize door, 1/3 chance.
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