Author: Uri Blass
Date: 08:40:02 04/28/01
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On April 28, 2001 at 11:17:15, Stephen A. Boak wrote: >On April 28, 2001 at 06:03:46, Uri Blass wrote: > >>On April 28, 2001 at 05:00:22, Dan Andersson wrote: >> >>>I remember that Ernst A. Heinz found diminishing returns. There are diminishing >>>returns in many other two-player games e.g. Reversi and Checkers. One possible >>>explanation for its absence is that chess evaluation functions are of a low >>>quality, because that chess is more complex. >>> >>>Regards Dan Andersson >> >>I chose the nunn position and not regular games. >>There is a reason for it. >> >>I believe that theory sometimes leads to relatively simple drawn positions if >>you search deep enough and it may explain diminishing returns when I believe >>that the nunn positions are more complicated and you may need more plies to get >>the draw when depth is not important so it is going to be more hard to prove >>diminishing returns on the nuun2 match. >> >>I believe that if I continue this nunn2 experiment to Deep Fritz depthes 3-15 >>and tiger14 depth 3-15 then diminishing returns will be demonstrated >>statistically. >> >>I am going to do it at least for depth 9-10 and I did not decide how much I am >>going to continue it(one reason is that the exact computer time that I need is >>not clear to me) >> >>Matches at depth 8 or even 9 can take a short time but matches at bigger >>depthes are going to take more time. >> >>I guess that the time that is needed after upgrading my hardware is something >>like 3^(d-9) hours per match at fixed depth d against smaller depth. >>and it means 27 hours per match at depth 12,243 hours per match at depth 14, >>729 hours per match at depth 15. >> >>If I play at least 11 matches at depth 15 in order to get 300 games for >>tiger(depth 15) and Fritz (depth 15) then I need something like 7290 hours that >>is >>almost a year of computer time. >> >>I am not going to give my computer more than an average of few hours in a day >>so I need some years to complete the experiment and it may be faster to wait for >>a faster hardware before starting matches at big depthes. >> >>Uri > >The problem is probably not the time per match. It is the huge quantity of >matches that must be played to observe any score other than 100% score for the >higher ply program and 0% score for the lower ply program, when the delta ply is >large. > >Don't forget, at ply delta of only 6, you already have a 50-0 score. The >relative Elo formula doesn't work for such a score. Maybe after a few hundred >games, the score won't be 100% to 0%, for ply delta of 6. But how bad will the >situation be with a ply delta of 8, 10, or 12? > >A bell-shaped curve isn't guaranteed to work at the extreme legs. It would be >foolhardy to rely on it working well in such cases. > >However, to extrapolate to a ply delta of, say 10, worse yet 15, how many >hundreds of millions of games will you have to play to not have a score of, say, >300,000,000 - 0. Even if future hardware plays such a match in 1 minute, you >will likely be a bit short in longevity to see a meaningful score other than >100% - 0%. > >I am exaggerating to some degree. If you play this many games, I believe all >programs will show a 'bug' somewhere along the line, and lose or draw a game or >two. But, do you honestly think that a program searching to delta ply depth 15 >(N+15) will ever 'normally' draw or lose to a program searching to only ply N? I believe that it dependent on N I believe that when N=10 N+15 plies can normally draw or lose against N plies(unfortunately there is no chance that I am going to play a game at depth 25 to prove it. I think that it is also possible that ply 3 will draw against ply 18 if it is lucky I looked at the games of 3 plies against 8 plies and in part of the cases when the 8 plies did not win it outsearch the 3 plies but unfortunately there was something deep that both sides did not see that caused the 3 plies to get the advantage. I remember one case when the deeper searcher suddenly saw that it is losing for something that the other program did not calculate. I believe that one game of tiger(8 plies) against fritz(3 plies) was a game with no tactical mistakes when the 3 plies was lucky to get to a closed position when the sides could not make progress. Uri
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