Author: Sune Fischer
Date: 09:12:22 02/07/02
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On February 07, 2002 at 11:34:12, Dann Corbit wrote: >On February 07, 2002 at 11:23:56, Sune Fischer wrote: >[snip] >>I don't understand why this is unsolved, we agree that there is DR in the lower >>plies. We can also agree, I think, that DR must become more and more difficult >>to measure as the whole thing converges to 50-50%. >>Of cause we cannot prove it empiricly without unlimited computing power, but all >>indications suggest there is continues DRs (by simple induction). > >I think that the induction is probably wrong. I suspect at some point, there is >not any further diminishing of the return. I base this wild extrapolation on >the shape of the graphs and nothing more. One thing for sure, intuition is >clearly wrong about it. I think there will be DR always. >>Unless chess happens to be tactics limited to ply 25 or something, I don't see >>what could upset the obvious conlusion. > >The current data does not support it (but is very inconclusive). > >>>Because chess is exponential, in 10 years we will see 5-10 plies deeper (if a >>>branching factor of 2 could be achieved it would be 10). >> >>Yes, and if you want to study the DRs between ply 21-22 and 22-23, it will >>require a million games to prove statisticly the expected 0.01% change in >>win-lose cases, good luck :) > >In both studies that I have seen, there is about 13% improvement for each >additional ply at the late plies. Consider that this is for EVERY MOVE. I >supect that the increase in play strength will be way, way more than 1%. In >fact, this is *exactly* what we see with increased ELO due to increased >computing horsepower. It seems that we increase 50 ELO or so with each doubling >of compute power. If there *WERE* diminishing returns, at some point, compute >power increases will have no effect on game play. I don't think that will >happen, but I am not basing this guess on hard data. Just an extrapolation from >the way my brain fits those graphs that I have seen. As far as I understand, the diminishing returns is not the 1st order effect of an elo increase, it is the 2nd order effect of the "change in elo increase". Ie. if plies 12-13 gives a lose-win of 45-55%, then this is equivalent to some rating difference. Now by going from 13-14, you _still_ get a good elo increase almost as much as before, but the relations may be only 45.5-54.5%. So the "change in the change" in win/lose is a mere 0.5%, very hard to measure. Of cause you can still observe the rating difference (ie. it helps to go one ply deeper), but it is very hard to prove, that it doesn't increase _as much as before_. And this second order effect that is what we call diminishing returns. It is probably magnitudes smaller than the change in elo, but it is there none the less. I hope you get the importent difference, I don't know how else to explain it ;) -S.
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