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Subject: Re: A ratio of exponentials

Author: Jeremiah Penery

Date: 17:27:03 01/27/00

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On January 27, 2000 at 20:01:55, Dann Corbit wrote:

>On January 27, 2000 at 19:25:40, Jeremiah Penery wrote:
>[snip]
>>This is what you originally wrote:
>>------
>>Do you know how Deep Blue searched?  How will we reach those fantastic speeds?
>>Faster hardware does not inflate ratings.  It raises it by a logarithmic amount
>>for each increase.  It is estimated about 50 ELO.  So, suppose we have a program
>>with 2500 ELO and we want to get to 2800.
>>2500 + 50ELO/doubling * 6 doublings = 2800.  Sounds pretty simple, right?
>>
>>But if it takes 500 Mhz to get 2500 ELO, then it will take:
>>
>>500 * 2 * 2 * 2 * 2 * 2 * 2 = 32 GHz to achieve it (roughly speaking).
>>
>>IOW, more horsepower is a tough way to make chess programs play better.  There
>>is also evidence (according to some) that the increase in speed has
>>*diminishing* returns.  Hence, it may take a terahertz to get there.  Don't know
>>of any material that could do that, not even a Josephson Junction.
>>------------
>>
>>When you're talking about increasing Elo, I assume that's in games with some
>>time control.  When you said that the increase in speed has diminishing returns,
>>I figured this was because of the exponential nature of the chess tree.  I.e.,
>>at some point, the increase in speed to see any gain will be prohibitively high.
>
>I don't remember where I read it, and I can't find the article now.  It may even
>have been discussions on this board.  As far as diminishing returns, I meant
>that you don't always get 50 ELO for the next ply.  At some point, maybe you get
>40, then later 30, etc.

I was taking your wording literally that *speed*, not *depth*, has diminishing
returns.  Because the speed has to go up exponentially to see more depth.  And
seeing more depth is the only way to get a better rating (using the same
program, of course).



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