Author: Tony Werten
Date: 03:06:44 04/29/04
Go up one level in this thread
On April 29, 2004 at 05:30:25, Uri Blass wrote: >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. > >I think that when we talk about diminishing return we are interested in time. >Suppose that you found a way to do your programs 2 times faster by some >optimizations. > >How much rating are you going to get from it. >If there is a diminishing returns then you get less from it when the time >control is longer so speed optimizations are mainly important for blitz. > >programs has nearly constant branching factor so saying that you search 1 ply >deeper is nearly the same as saying that you have a machine that is 2.xx times >faster. Yes, speed optimisations are comparable with d vs d+1 matches ( or rather d vs d+0.05 ) and therefore have diminishing returns as well (IMO) and also give more at lower depth. Wether or not search enhancements and evaluation improvements also have this is hard to tell since nobody has researched that yet. Shouldn't be to hard. Just do matches were the relative advantage stays the same ( ie 2 vs 3, 4 vs 6, 6 vs 9 ) and you have yet another thesis. Tony >> >>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
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