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Subject: Re: A ratio of exponentials

Author: Jeremiah Penery

Date: 14:37:05 01/27/00

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On January 27, 2000 at 14:31:59, Dann Corbit wrote:

>The base argument assumes that speed increases exponentially (Moore's law).  If
>speed increases exponentially and chess is an exponential problem, then there is
>a linear increase in a program's ability to solve.

Not if chess grows with a higher exponent than speed...

Let's assume a branching factor of exactly 3, for simplicity.  This is a little
high for today's programs with good pruning schemes (as Ernst pointed out), but
it's still pretty good.
I'll also assume a starting point of 100 MHz (again, for simplicity in
multiplication).

Ply 10 takes 3 minutes to complete, after ply 9 is already completed.
This means ply 11 will take 9 minutes, ply 12 will take 27 minutes, and ply 13
will take 81 minutes.

In order to be able to complete ply 11 in 3 minutes, the processor speed will
have to be increased to 300 MHz.  For ply 12, 900 MHz, and 13, 2700 MHz.

Since we are talking about an actual playing strength increase, as in real
games, this time becomes critical.  The only time a program's strength can
increase is when it reaches a new depth.  Since the speed required to reach any
new depth within a certain time limit is increasing with a factor of 3, this
will become prohibitive fairly quickly:

Ply 14: 8100 MHz
Ply 15: 24300 MHz
Ply 16: 72900 MHz
etc...

Let's assume each ply is worth 100 Elo (for simplicity), with one ply being
1200.  For 2200 Elo, you only need 100 MHz, or 22 Elo/MHz.  2300 Elo will
require 300 MHz, or 7 2/3 Elo/MHz.  2400 needs 900 MHz, or 2 2/3 Elo/MHz.

As you can see, the increasing speed is giving diminishing returns in strength,
when a given time control is being enforced.


Is there something simple I'm just missing here?

Jeremiah



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