Author: Tony Werten
Date: 06:57:12 02/06/02
Go up one level in this thread
On February 06, 2002 at 09:13:40, Uri Blass wrote: >On February 06, 2002 at 08:42:00, Tony Werten wrote: > >>On February 03, 2002 at 17:25:48, Wylie Garvin wrote: >> >>>On February 03, 2002 at 13:32:42, William H Rogers wrote: >>> >>>>Here is an item from Chess Skill in Man and Machine >>>>One of the first programs written for computers and later turned into Deep Blue >>>>well, I least I think that it lead to Deep Blue. >>>>The ran a series of 300 games, playing the program against itself with only >>>>different ply settings to see the difference in playing strength. >>>>Here are the results: >>>> >>>> Rate P4 P5 P6 P7 P8 P9 >>>>P4 1235 -- 5.0 .5 0 0 >>>>P5 1570 15 -- 3.5 3.0 .5 0 >>>>P6 1826 19.5 16.5 --- 4.0 1.5 1.5 >>>>P7 2031 20 17 16 --- 5.0 4.0 >>>>P8 2208 20 19.5 18.5 15.0 --- 5.5 >>>>P9 2328 20 20 18.5 16.0 14.5 --- >>>> >>>>As you can see in the lower ply numbers the program gained the most strenght, >>>>but as the ply level got higher the rating increase became smaller and smaller. >>>>It would be nice to see some math on a curve to estimate the over all effects. >>>>Bill >>> >>>Hi, >>> There's a 1997 paper by Schaeffer et. al. that refutes the idea that the >>>increase in strength is constant per ply at high search depths. They suggest >>>that there are diminishing returns for deeper search, and that previous research >>>didn't reveal it simply because chess programs make lots of evaluation mistakes. >> >>They are wrong. Suppose my program does get twice as strong with every extra >>ply. How are you going to measure it ? >> >>We play 10 games. First I win 1, then I win 2, then 4, then 8. Quite impossible >>for me to keep improving at this level ! > >No >This is not the way to check. > >do a match between your program and itself > >4 plies against 3 plies >5 plies against 4 plies >6 plies against 5 plies.... > >If you find that the result at big depthes is closer to 50% then it means that >there is an evidence for diminishing returns. Maybe. It might mean the deeper searching program gains less, it might also mean that the difference is smaller. in 4-3 the deeper program searches 33% deeper than the shallow one. In 6-5 that's only 20%. Sounds logical to me that 4-3 should score more than 6-5. It has (IMO) nothing to do with diminishing returns. If 8-6 scores worse than 4-3 then I'd agree. Tony > >Note that diminishing return should happen after enough plies because after >enough plies because it is impossible to play better than the best moves so >after enough plies the program is going to practically solve chess. > >The only question is not if there is diminishing returns but how many plies do >you need to find diminishing returns. > >It may be also interesting to know what is the situation in other games like go. > >Uri
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