Computer Chess Club Archives


Search

Terms

Messages

Subject: Re: ply search vs elo rating - proposed formula

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



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.