# Re: I strongly disagree with Lee's answer

From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Fri May 11 2001 - 22:15:18 MDT

Spike Jones wrote:
>
> "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.

In this instance, where Monte's actions are fixed, *and the door he
reveals is predetermined*, the problem is equivalent to the
lightning-strike riddle that Lee asked. The card he turns over may have
'C' written on it. In this case, if he reveals 'A', there is no reason to
switch.

> 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.

Who says that Monte *must* open a door? If I choose C and it's a failure,
Monte can simply not open any doors at all. He only has a logical
motivation to open a door, possibly causing a change in my actions, if he
wants me to switch; he only wants me to switch if C actually has the
prize. Of course, if Monte realizes that I know this, and I have
correctly picked C, he will fake me out by showing me B. This is why
Bayesian reasoners should never play zero-sum-games with each other.

-- -- -- -- --
Eliezer S. Yudkowsky http://singinst.org/
Research Fellow, Singularity Institute for Artificial Intelligence

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