Author: Robert Hyatt
Date: 08:00:25 05/05/01
Go up one level in this thread
On May 05, 2001 at 09:40:01, Ralf Elvsén wrote: >On May 05, 2001 at 08:46:52, Jesper Antonsson wrote: > >>On May 05, 2001 at 00:53:39, Robert Hyatt wrote: >>>On May 05, 2001 at 00:20:16, Peter Kappler wrote: >>>>>OK... then at _today's_ computer speeds, I don't believe in diminishing >>>>>returns yet. In 20 years, perhaps. But the difference between a 15 ply >>>>>search and a 17 ply search is _significant_ still. Lots of experiments have >>>>>shown that diminishing returns don't appear to happen at any depth we can >>>>>reach today, even using 24 hours of computer time. >>>> >>>>What about Ernst Heinz's fixed-depth, self-play matches with Fritz? They >>>>seemed to strongly suggest diminishing returns, even at depths much >>>>shallower than 15 or 17 plies. >>>> >>>Perhaps the program? Hans Berliner did an interesting experiment a long while >>>back, and concluded that "dumber" programs show this diminishing return problem >>>sooner than "smarter" programs. Ernst also concluded that for the time being, >>>at least thru 15-16 plies, there was no apparent 'diminishing returns' for his >>>program when he replicated the tests Monty and I did... >>> >>>I don't say there is no diminishing return. I say I don't see any real >>>evidence to support the idea just yet.... >> >>I disagree. In Ernst Heinz's experiment "Dark Though goes Deep" >><http://supertech.lcs.mit.edu/~heinz/dt/node46.html>, and in a similar >>experiment before his that you did with Crafty, the rate of best-move changes >>from one ply to another clearly went down as depth went up. The margin of error >>is a bit high to draw any real conclusions from the changes at the greatest >>depths, but the trend is clear nonetheless. >> >>Furthermore, I think that experimental data is not really needed, diminishing >>returns in this sense (in a rating sense, I have no idea, however) must exist. >>The deeper you go, the more best moves will be found for the right reasons (and >>the more inferior moves will be discarded), and after that the best move >>returned won't change (as much). >> >>When I fit an exponential curve to Heinz's results (and extrapolate), I get >>approximately these best change rates: >> >>1 >>2 37,5% >>3 34,6% >>4 31,9% >>5 29,4% >>6 27,1% >>7 25,0% >>8 23,0% >>9 21,2% >>10 19,5% >>11 18,0% >>12 16,6% >>13 15,3% >>14 14,1% >>15 13,0% >>16 12,0% >>17 11,0% >>18 10,2% >>19 9,4% >>20 8,6% > >Bold extrapolation... :) > >> >>This means that going from ply 9 to 10 gives about as much as going from ply 17 >>to 19. The returns are still great on the depths where programs usually play >>today and the returns taper off very slowly, but I'm convinced they *do* taper >>off. >> >>Jesper > >I have yet to see a convincing argument why the rate of best-move changes >would be so directly related to playing strength. If you believe that another ply gives a more accurate answer, which I do, then the rate of change should be obvious. If you change your mind, you find a better move due to the deeper depth. > >I think Ernst's self play experiment with Fritz is the one to look at since >he addresses the immediate question, and >he thought it proved diminishing returns to a certain degree. That one or >two extra plies gives a benefit is of course true, the question is how much. > >Ralf
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