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, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote:
----- Oorspronkelijk bericht ----- Van: Matt Gokey <[EMAIL PROTECTED]> 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 _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
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