Author: Francesco Di Tolla
Date: 01:50:35 07/16/99
Go up one level in this thread
>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
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