Author: Sune Fischer
Date: 15:03:41 02/06/02
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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.
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