Author: Graham Laight
Date: 03:52:53 10/21/99
Go up one level in this thread
On October 20, 1999 at 19:27:26, Jeremiah Penery wrote: >On October 20, 1999 at 16:27:23, Joshua Lee wrote: > >>>>>>This would yield the following results: >>>>>> >>>>>>Ply Elo Rating >>>>>>=== ========== >>>>>> >>>>>>2 1098 >>>>>>4 1386 >>>>>>6 1635 >>>>>>8 1855 >>>>>>10 2052 > >> ????????? Awhile back i posted where hiarcs played the exact first 6 moves of > two different IM's for whites first six moves and blacks first 5, this is too > low. > >Hiarcs searches exactly 10-ply? Also, just because 6 moves were the same, does >not mean _all_ the moves were the same. Further, these numbers were figured >using K=0.15 for the chess-knowledge. Hiarcs may have either more or less, and >so it is impossible to tell actual numbers for any program. > >>>>>>12 2230 >>>>>>14 2392 > >> Again this is too low Deep Blue was atleast 2650 searching 14ply > >Deep Blue did not search only 14-ply. It did 14-ply brute-force, plus 30+ ply >of extensions in most of the interesting lines. Not to mention that DB would >probably have a K-value of greater than 0.15, which would make all the ratings >on this list go up for each depth. However, I suspect that the ratings may >level out a bit at the top, because the maximum theoretical ELO rating is >somewhere around 3000, I believe. > >>>>>>16 2542 >>>>>>18 2680 > >> That makes these atleast 300 or more elo points too low > >See above. > >>>>>>20 2809 >>>>>>22 2929 > >>Otherwise good idea rework the numbers and we have a good indicator of strength >>vs ply. >>also at 1 ply Hiarcs was winning 3 out of 4 games against me so maybe at 1 ply >>it is 1700 but again this is all relative to the time control. Are we talking >>3min per move? > >Again, 1-ply doesn't necessarily mean exactly 1-ply. It means 'at least' one >ply. There are always extensions and quiescence search to achieve greater >apparent depth. > >Jeremiah 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. 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: 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. Graham
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