[CrackMonkey] Re: A cool problem

[Seth David Schoen]

Monkey Master writes:

> begin  AOLMonkey quotation:
> > It kind of depends on how, exactly, the adversaries are going to
> > behave.  Otherwise you could say loudly, "We'll just all guess RED!
> > That way half of our guesses are guaranteed to be right."  Since the
> > adversary has sworn to kill the maximum number of people, they'll
> > put everyone in blue hats.
> 
> 	I figured that I'd do this, originally.
> 
> 	We all agree to answer red.  The first person, upon seeing
> that all the hats are blue will answer "BLUE!" and hope that everybody
> gets the hint all the way down the line.  Most people will see many
> blue hats and probably figure it out.

Remember that the adversary can hear this conversation. :-)

Actually, that gets into a sort of Newcomb's Paradox question.  The
adversary has heard what is purportedly a complete description of a
strategy and intends to pre-arrange things so as to defeat that
strategy...

As I pointed out in mail to David, it wasn't specified whether the adversary,
in trying to maximize the number of people killed, is maximizing

- the minimum number of people guaranteed to be killed,
- the maximum number of people who _might_ be killed in some situation, or
- the expected number of people killed

The distinction only matters if there is some unpredictable or chance
element which isn't part of the communicated strategy.

Even with that distinction, I don't believe that there is any way of using
chance or intuitiion to improve a strategy beyond what can be communicated.
It might be that, by saying that, I have just taken a position on the
Church-Turing Thesis or the resolution of Newcomb's Paradox, but I was
mainly just trying to say that I don't think you can cheat the adversary by
leaving some part of your behavior unspecified, or using your intution to
deviate from what you said you would do.

-- 
Seth David Schoen <schoen at loyalty.org>  | And do not say, I will study when I
Temp.  http://www.loyalty.org/~schoen/  | have leisure; for perhaps you will
down:  http://www.loyalty.org/   (CAF)  | not have leisure.  -- Pirke Avot 2:5