Author: Jeremiah Penery
Date: 14:37:05 01/27/00
Go up one level in this thread
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
This page took 0 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.