Author: Jeremiah Penery
Date: 10:37:12 10/20/99
Go up one level in this thread
On October 20, 1999 at 11:03:20, Graham Laight wrote: >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 makes sense now. :) >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. How many % of all useful chess knowledge would you say the best humans (Kasparov, etc.) have? Will your equation work in their case, since they obviously have a much greater number than computers? >>>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. So how much knowledge are you saing Rebel has? I'm not understanding this relation. :/ >>>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. I thought this was the wrong way to do it. :)) The only way to determine whether these numbers hold up is by trying it on all sorts of humans and computers, to see whether it accurately predicts the ratings. :) >>>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. Yes, thank you. :) Jeremiah
This page took 0.01 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.