From: Adrian Tymes (wingcat@pacbell.net)
Date: Fri May 11 2001 - 23:37:59 MDT
"Eliezer S. Yudkowsky" wrote:
> "Emlyn (onetel)" wrote:
> > Eliezer 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.
> >
> > On ExtroQuiz, if you pick door C, and the prize is behind door B, apparently
> > the gameshow host does not open door A and show that it is empty. What,
> > then, does the host do instead?
>
> Nothing - just says "Is that your final answer?" in portentous tones, with
> no accompanying demonstration or additional information. He doesn't
> *want* you to change your choice.
...unless ve knows that contestants would know this, and thus take no
opening as a cue to switch (.5 chance vs. 0 chance of prize). On
ExtroQuiz, the host knows that the contestants have done all the
second-guessing that matters, and thus know the host's algorithm (or
lack thereof). Given that, how can the host act so as to minimize the
guest's chances of winning if:
a. the guest picks the prize door?
b. the guest picks a non-prize door?
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