Author: Uri Blass
Date: 06:13:40 02/06/02
Go up one level in this thread
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. 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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