[computer-go] an idea... computer go program's rank vs time

[Nick Apperson]

you are right about my math being wrong.  I wasn't paying that much
attention to that step, but with the correct math (as was pointed out) you
end up with a linear equation assuming what I said to assume.  Man, its only
been a couple years and my precalc skills have gone to crap...  Thanks for
the correction.  And Dave, you said what I was trying to say, except
better.  The only thing I have to add is that one major difference between
humans and computers is that brains are able to think in parallel much more
effeciently.  For a game such as go, we are able to use that ability more
because of the larger branching factor.

On 1/23/07, dave.devos at planet.nl <dave.devos at planet.nl> wrote:
>
> ----- Oorspronkelijk bericht -----
> Van: Matt Gokey <mgokey at charter.net>
> Datum: maandag, januari 22, 2007 9:59 pm
> Onderwerp: Re: [computer-go] an idea... computer go program's rank vs
> time
> > Nick Apperson wrote:
> >
> > > He is saying this (I think):
> > >
> > > to read m moves deep with a branching factor of b you need to
> > look at p
> > > positions, where p is given by the following formula:
> > >
> > > p = b^m (actually slightly different, but this formula is
> > close enough)
> > >
> > > which is:
> > >
> > > log(p) = m log(b)
> > > m = log(p) / log(b)
> > >
> > > We assume that a doubling in time should double the number of
> > positions
> > > we can look at, so:
> > >
> > >
> > > m(with doubled time) = log(2p) / log(b)
> > > m(with doubled time) = log(2) * log(p) / log(b)
> > Your math is wrong (I think).
> >
> > The correct equivalency for the last line would be:
> > m(with doubled time) = (log(2) + log(p)) / log(b)
> >
>
> Yes. Don's scalability argument states that ELO gain is proportional
> to time doubling.
> For me scalable use of time implies that time translates into depth.
> The extra depth is:
>
> m - m0 = log(2)/log(b).
>
> So if the ELO gain for time doubling in Chess equals 100 over a wide
> time scale and if Go has a 10 times larger branching factor than
> Chess, then the ELO gain for time doubling in Go would equal 100/log
> (10) = 43 (everything else assumed equal).
>
> I'm not sure i agree with Don, but i just want so say that if he is
> right, than mathematically he is also right with a larger branching
> factor.
>
> Dave
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