Author: Ralf Elvsén
Date: 08:28:33 05/05/01
Go up one level in this thread
On May 05, 2001 at 11:00:25, Robert Hyatt wrote: >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. Of course, I should have explained myself better: the quantitative relation is not known, i.e. how does the increase in playing strength relate to this change-your-mind-rate. This is only guesswork as far as I know. If another ply is better, you must change your mind sometimes. That the reverse is true isn't clear to me: change your mind to a move that doesn't change the outcome of the game (on average). I don't like this unclear link. We may have diminishing return between (say) ply 15 - 20 and yet have a constant rate of new best-moves, or (more likely) it may decrease but much slower. Ralf > >> >>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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