Author: Tony Werten
Date: 07:30:15 02/06/02
Go up one level in this thread
On February 06, 2002 at 10:08:25, Sune Fischer wrote: >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. Doesn't make a difference. Depth and number of nodes are the "same". >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. Ok, have it your way. in 4-3 you give BF/3BF advantage and in 5-4 you give BF/4BF advantage. The ratio is constant, but the added percentage isn't. New example: distance 100 miles. 10 Mph=> 10 h 20 Mph=> 5 h 30 Mph=> 3.3 h 40 Mph=> 2.5 h New paper. Diminishing returns in carspeed ? Tony > >The diminishing returns issue is probably an effect of converging towards the >ideal move as often as possible. > >-S.
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