On Tue, 2007-01-23 at 21:08 +0100, [EMAIL PROTECTED] wrote: > 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.
It's trivial to prove programs are infinitely scalable. It's a bit more difficult to prove humans are - but I think it's probably a similar proof. I believe a scalable program can be "highly scalable" or "less scalable" meaning they improve less or more with time. Humans appear to be of the "highly scalable" variety, at least in chess they improve with time faster than computers do. A chess program playing at 3 minutes per move is about 300 ELO stronger than the same program playing at 5 seconds per move. A human is more like 400-500 ELO stronger. There is strong evidence that in chess this doubling tapers off at strong levels. This makes a great deal of sense. Ernst Heinz did some experiments that proved empirically (with high statistical confidence) that strength tapers off with search depth in computers. Although he measured this using search depth, I believe the tapering is more related to strength. It just happens that the deeper searching programs were playing stronger. If someone could construct a computer that played just as well with half the search depth, I think the tapering would be approximately consistent with the deep searching program of similar levels. The tapering is very gradual and even at high ply depths the ELO improvement for a doubling is quite good. That's why I believe in GO it will be hard to see this tapering effect. I believe GO players are farther from the ultimate top that chess players (I mean the very best players.) Once you are playing almost perfectly, you won't get quite as much from the extra thinking time. I did an experiment long ago with a checkers-like game I made up. It is simple checkers on a 6x6 board and only 1 jump allowed. It's possible to construct an enormously deep searching program with this little mini-game. I also found that the really super deep levels taper off, and yet it is gradual and you never seem to stop benefiting measurably from each additional ply of search. The program searches deep enough that it's easily to imagine that it can't make errors, but obviously one side is making errors. The worlds best checkers program are like this too. They go much deeper than in chess and they are quite amazing how deeply they search. I think they are way beyond human strength now, but they still lose games to each other and make mistakes that 1 more ply of search would solve. That's really the point - 1 extra ply always solves a thick layer of problems that you couldn't solve before. - Don _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
