"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.
This is a tricky game that illustrates how very poor is the human
brain for understanding stochastic processes. The door switching
strategy holds only if Monte *always* opens a zonk door and
gives you a chance to switch.
Imagine the game is restated thus: you pick door C. Then Monte
says "Eliezer, if I agree to reveal door B, will you switch to door A?"
Then one is left second guessing a possibly malevolent game host.
Since we are discussing probabilities and things that can easily
be calculated, heres one for you: suppose you choose a number
randomly (x), you know that the probability of its being prime
is about 1/ln(x). OK, suppose you pick two random primes and
multiply them together to get a composite C. What is the probability
that C+2 is prime? Is it still 1/ln(C+2) ?
The answer to this is not trivial, and it bears directly on the discussion
on page 87 of Damien's updated version of The Spike. spike
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