Author: Odd Gunnar Malin
Date: 17:03:10 02/06/02
Go up one level in this thread
On February 06, 2002 at 18:03:41, Sune Fischer wrote: >On February 06, 2002 at 17:43:09, Dann Corbit wrote: > >>On February 06, 2002 at 15:35:28, Sune Fischer wrote: >>[snip] >>>Well I don't disagree with that, but suppose in any position we knew what the >>>best move(s) was. Now how often would a n-ply search find the correct move(s)? >>>This will give some kind of probability distribution on the plies. I'm sure this >>>is directly related to the diminishing returns at the higher plies. >> >>Diminishing returns at higher plies has not been demonstrated. The research by >>both Heinz and Hyatt is statistically inconclusive. >> >>If you make a program with a material only eval, it will swim through plies like >>a salmon on steroids. And it will lose all of its chess games to programs >>searching half as deep. >> >>IOW -- plies don't tell the whole story. And what happens when we gain another >>ply is still somewhat mysterious as far as what the value should be. > >Pure speculation on my part here, but if the program did a brute force search >to ply n (no extensions), using only material evaluation, then it should be >possible to prove diminishing returns(?) (see below). > > >>Here is a puzzler... >>When we search another ply, we typically expend more effort than all the >>previous plies combined. Why is it (then) that instead of being at least twice >>as good in the evaluation, we are only fractionally better? After all, we are >>looking at exponentially more board positions. It's a bit odd that our strength >>does not increase at least linearly (or does it, at some point?) >> >>The strength increase looks a bit like a decaying exponential (considering the >>graphs from available research papers and ignoring the enormous error bars). > >Yes, that is actually what I've been trying to explain. >I think I understand the nature of that decaying/descending sequence. > >Suppose you have millions of given random test positions in which you *know* the >best move(s). >Now run tests to see how often a 1-ply search will find the correct move, and >how often a 2-ply search will find the correct move etc. >Line up all these percentiles, and you will probably get something like this: > >1-ply search: 40% correct moves >2-ply ......: 55% correct moves >3-ply ......: 65% correct moves >4-ply ......: 72% correct moves >etc... > >The thing is, that the percentiles _must_ converge towards 100, so it will need >to slow down, there may only be 2% difference between a 12 and 13 ply search, >which is why it is really hard to measure anything. > >-S. This would tell you that a 10 ply search is better than a 9 ply search but how should you calculate the strenght out of this? Correct moves is a linear scala but why should the strength difference between 20% and 30% be equal to the strength difference between 80% and 90%. With this selfplay test we already have a scale for strength (rating). Odd Gunnar
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