Author: Sune Fischer
Date: 07:08:25 02/06/02
Go up one level in this thread
On February 06, 2002 at 09:57:12, Tony Werten wrote: >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 So it would seem, but the search is exponential and not linear. I think you should not consider the "depth" but rather the number of nodes searched. If you go one ply deeper then (assuming your branch factor (BF) is not too depth dependent) you a factor of BF more nodes, this ratio is fairly constant so I'd go with Uri's definition. The diminishing returns issue is probably an effect of converging towards the ideal move as often as possible. -S.
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