Author: Graham Laight
Date: 09:18:58 10/21/99
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On October 21, 1999 at 09:19:11, Jeremiah Penery wrote: >>Firstly, one of you said that there was a theoretical max elo rating of 3000. >>Presumably, this is calculated by correlating elo rating with proportion of >>draws achieved between 2 players of that level. Is this correct? Has anyone done >>this work. > >I'll try to look up where I found this... It wasn't exactly 3000, I think, but >somewhere around that number. > >>Secondly, the time the computer takes theoretically doesn't matter (though it is >>well known that if a computer plays quickly, the human opponent tends to play a >>lot worse). >> >>Thirdly, in view of the estimated figures for Hiarcs shown above, I have decided >>to modify Laight's equation as follows: > > >Hiarcs may simply have a greater K than 0.15, which you were using before. DB >almost certainly does. Although the new formula looks pretty good. :) > > >>Laight's Equation >>================= >> >>Version 2: 21/10/99 >> >>elo rating = log((Ply * K * C1) + C2) * C3 >> >>Where ply = ply search depth >>K = Knowledge Level >>C1, C2, C3 are constants. >> >>The extra constant, C1, is necessary to compress the range of results being >>produced. >> >>As before, K is calculated as follows: >> >>Kn = % of all the useful chess knowledge the program has >>K = Kn/(100 - Kn) >> >>If C1 = 0.1, C2 = 1.3, C3 = 13500, and K = 0.2, this yields the following >>results: >> >>Ply 1 elo = 1628 >>Ply 10 elo = 2377 >> >>This is well in line with the numbers Joshua Lee suggested above. >> >>If Laight's equation applied to Hiarcs and Deeper Blue is accurate, it implies a >>K of 0.2, which would mean that both computers have about 17% of all the useful >>chess knowledge. > >DB has a lot more knowledge than Hiarcs does. Also, DB was searching a lot more >than the 14-ply that Joshua was saying - it searched 14 + 30(+) ply in most >interesting lines. It's really difficult to determine an accurate 'depth' most >of the time, because for each program it will be different, based on the number >of extensions done. Hiarcs probably extends more than most other micro >programs, but DB does a lot more even. > >Unfortunately, this formula probably won't work for humans, because it's >impossible to determine a search depth. Therefore we can't use humans as a >gauge for the accuracy of the 'K'. > >I figured for myself that I have only 5% of chess knowledge (K=0.05), and that I >search 2-ply. Based on this, I got a rating of 1583. This is a bit too high, I >think. :) > >Jeremiah I must admit I'm having difficulty making the numbers behave correctly in the light of this new information. I'll keep working on it...
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