Author: Ralf Elvsén
Date: 06:40:01 05/05/01
Go up one level in this thread
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. 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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