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

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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