Author: Anthony Cozzie
Date: 05:40:03 04/29/04
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On April 29, 2004 at 03:13:07, Tony Werten wrote: >Hi all, > >a while ago we had some discussions about diminishing returns in search for >chess. > >My opinion was that you can't prove that with programs searching d vs d+1 ply >depth because the advantage of the d+1 program gets smaller. ie at d=1 it has a >100% depth advantage, at d=2 it's 50% etc. > >Some people claimed that you can't compare it that way because bla bla >exponential something bla :) > >Well, I found an easier way to explain it. > >A few assumption: > >The easiest way to win is when you see a trick, your opponent doesn't see. > >The depth that needs to be searched to see a trick is equally divided. ie there >are as many tricks hidden 1 ply away as there are tricks at 2 ply ( it doesn't >really matter but it's easier to visualize ) > >w is player d+1 >b is player d > >d=1: b sees tricks 1 ply away, w sees ply 1 and 2 => w sees 2.0x as many tricks >d=2: b:1,2 w:1,2,3 => w: 1.5x >d=3: b:1,2,3 w:1,2,3,4 => w: 1.3x >... >d=10: b: 1..10 w: 1..11 => w:1.1 x > > > >Conclusion: There may or may not be diminishing returns in chess, but d vs d+1 >are not going to prove it, because those matches by itself are a clear example >of diminishing returns regardless what game is played. > >disclamer: I know chess isn't only about tricks, but it is an advantage to see >more of them then your opponent. Clearly the win percentage is depending on >other (random) stuff as well. BUT When you see less more, the advantage becomes >less. > >Tony I'm not even sure I agree with "the tricks are equally divided". It would be possible to get some sort of statistics for this, but my guess is trick % declines with depth :( Even so, just the extra positional help makes more depth worth it IMO. anthony
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