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

Author: Jeremiah Penery

Date: 10:37:12 10/20/99

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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



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