Author: Robert Hyatt
Date: 11:37:55 03/29/01
Go up one level in this thread
On March 29, 2001 at 12:54:59, José Carlos wrote: >On March 29, 2001 at 11:22:49, Robert Hyatt wrote: > > I am one of those who "feel" that the behaviour must be asymptotic. Actually, >I have absolutely no proof to support my feeling, but at least, some reasoning: > > - Doubling speed is, on average, less than an extra ply, given the actual >branching factors. So, as the tree grows faster than we go deeper, we are >deepening more slowly every time we double speed. > - Even if we could achive a bf of 2, so that doubling speed would give a >constant ply deepening, we could discuse if a ply add is worth the same at ply 7 >or at ply 40. Again, no proof exist, but I tend to feel that something that is >40 deep in the tree has less influence than something that is very near, >specially considering that, if I search 40 moves deep, probably I'm gonna win >every game, so it doesn't matter much if I see 40 or 41; I'll win anyway. OK.. but since the doubling is happening at a linear rate, let's do tripling which _does_ give an extra ply. So each time the speed triples, we go one ply deeper, and this goes on forever. In fact, I am reasonably sure that as the search goes deeper and deeper, the effective branching factor goes down somewhat due to more transpositions. And yes, once you get to a "critical depth" then going deeper won't help. The question of "what is the critical depth?" is an open one, however. We are a long way from 40. in fact we are closer to zero than 40 at the present. > >>yes, it is very probable that 20 years ago a doubling would be worth more >>than 70 points. But it seems to have stabilized to around 70 for a long >>while now. > > Yeah, it's a normal behaviour of an asymptotic curve. It's slowly flattening. > >>And no, I am _not_ talking about each doubling walking the computers up the >>FIDE rating list by 70 points. I doubt doubling is worth much at all when >>playing humans in the top 30 or so. But in pure comp vs comp games, give >>me that factor of 2x every time. It will swing the balance in my favor for >>a long long time I think. > > This is what I've said for some time. IMO, in comp-comp, small differences in >playing strength make big difference in rating points. It seems that the scale >is different. That's why it is impossible to compare ssdf and fide ratings, >unless without doing some calculations. It's something like celsius and >farenheit degrees: different scales, different starting points. If we could take >a given program's ssdf and fide rating (in this second case, based upon a big >number of games against humans) and the same with another program, we could >extrapolate the fide rating for any program between them both in ssdf (I hope my >bad english is not bad enought to not being undestood). > Anyway, chess is much more complicated than degrees transformations, so we >could only expect an approximation, and we'd need a big number of games. > > José C. Had no problems with your English at all. In fact, I have had _more_ problems with American students at times. :)
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