Author: Graham Laight
Date: 08:03:20 10/20/99
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On October 20, 1999 at 10:16:12, Jeremiah Penery wrote: >On October 20, 1999 at 06:26:58, Graham Laight wrote: > >>On the basis of what I have read in these threads, I propose the following >>formula for the relationship between ply depth and elo rating: >> >>log((ply * K) + C1) * C2 >> >>Where ply = depth to which the search is 100% complete >>K = Knowledge level of program >>C1 and C2 are constants >> >>K is calculated as follows: >> >>If T is the total of all chess knowledge, and KP is the knowledge level of the >>program, then K = KP/(T - KP) > > >K and KP are both equal to the knowledge level of the program? How do you >determine KP? Is T equal to 1? Oops! Self referencing in the equation there. Sorry. In reality, you can't determine KP - you can only guess. The idea is that KP specifies how much of all useful chess knowledge the program has. You may, if you wish, work in percentages. So if a program has 13% of all possible useful chess knowledge, then K = 13/(100 - 13) = 0.15 This calculation is necessary to emphasise that as a program's knowledge gets closer to 100% of all useful chess knowledge, the ELO rating rises very rapidly. When the program has 100% of all useful chess knowledge, it's elo rating goes infinite in this case. >>Needless to say, the formula does not take account of search extensions (except >>that you can adjust the knowledge rating according to the cleverness of the >>extensions). >> >>I name this formula "Laight's Equation - 20/10/99" > > >:)) > >>To illustrate the formula in action, I will use the following values: >> >>K = 0.15 > > >Is this a low-knowledge program? I would guess that a program which has 13% of all useful chess knowledge would be a very high knowledge program. After all, Rebel searches about 200,000 nodes per second (nps), and cannot beat grandmasters who are looking at 3 nps tops. > > >>C1 = 1.5 >>C2 = 4300 > > >What made you pick these numbers? I used the scientific discipline of fiddling with the numbers until they looked about right. > >>This would yield the following results: >> >>Ply Elo Rating >>=== ========== >> >>2 1098 >>4 1386 >>6 1635 >>8 1855 >>10 2052 >>12 2230 >>14 2392 >>16 2542 >>18 2680 >>20 2809 >>22 2929 > > >That looks quite interesting, and probably quite accurate. :) The only things I >wonder are how you got the C1 and C2 values, and exactly what K=0.15 means. > >Jeremiah Hope I've clarified this somewhat. Graham
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