Author: Will Singleton
Date: 07:41:33 07/16/99
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On July 16, 1999 at 04:50:35, Francesco Di Tolla wrote: >>Thanks for your comments. Let me see if I understand you. Because the rating >>scale goes from like 2000-2800, but the mhz varies from 133 to 550 or so, >>there is too much variation in mhz relative to rating and that will skew the >>results. > >Well not really becuase of that: we know that the number of positions grows >exponentially with the number of moves. So doubling the clock (say from 200 to >400 or from 500 to 1000) does not double the depth reached. > >To make this "linear" you need to invert the funcciotn, and take the log of the >speed. This is a real measure of the pure brute force capibitliy in terms of >calculations. >So I would guess that: > >log(MHz) is nearly proportional play depth > >well this is not exact, since changing from pentium to pentium II or from >pentium II to pentium III also the design change of the CPU might make some >difference, but to a first approximation, it sould work. > >Now you should also "linearize" the scale of elos, but the range over which >you're looking is not to wide, so it looks probably linear. Of course including >a programs which play say, 1400 ELO, could chande the thing, but for a >relatively narrow range around 2500 ELO it doesent do to much difference. > >I think that might be right, if that's what you mean. >> >>Example: >>Rating mhz R/mhz R/log(mhz)/100 >> >>2200 200 11.00 9.56 >>2200 300 7.33 8.88 >>2200 400 5.50 8.45 >> >>2450 200 12.25 10.65 >>2450 300 8.17 9.89 >>2450 400 6.13 9.42 >> >>2700 200 13.50 11.73 >>2700 300 9.00 10.90 >>2700 400 6.75 10.38 >>2700 500 5.40 10.00 >>2700 600 4.50 9.72 >> >>One can see the benefit of your suggestion. Using R/mhz, it's about equivalent >>for an account to get 2200 using 400mhz as it is for one to get 2700 at 500mhz, >>which is clearly wrong. > >sure this is wrong > >>But r/log(mhz) method handles it correctly. It also >>handles the case when comparing 2200 at 200mhz vs 2700 at 600mhz. >> >>Would there be a better formula to use, or is that sufficient? > >Well it is much better, but in my opinion,looking at you numbers, it is still >not enough. > >TCB is today neaklry 2600@200MHz, this would imply ~2940@400 MHz,something that >I strongly doubt. > >There are at least two faults: > >- first we neglect the nolinearity of the ELO scale >- second we assume that raw power i relartetd to ELO, whic is true only to some >extent, i.e. we know that chess is not only tactics. > >The best way to thes this is to test this gainst Crafty: look at as much >different accounts running crafty you as you can and plot the elo they have >against the speed in MHz, you should be able to get some idea of the funztion >dependence. (please neglect accounts running weakened veriosn of crafty or fancy >books....) > >regards >Franz I have obtained a long list of crafty bench scores from Dann Corbit, all kinds of processors. I need a couple more, then I'll think about using those instead of mhz. One problem with that could be Crafty's bitboard method. It's possible a conventional program would yield different results, favoring one processor or compiler over another. otoh, it would account for multi-cpu systems. Will
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