Author: Jeremiah Penery
Date: 23:45:39 01/26/00
Go up one level in this thread
On January 27, 2000 at 02:02:24, Ernst A. Heinz wrote: >On January 27, 2000 at 01:49:31, Ernst A. Heinz wrote: >> >>On January 27, 2000 at 01:42:46, Jeremiah Penery wrote: >>> >>>And if you have to increase the speed exponentially just to see any gain at >>>all, that's still diminishing returns compared to the >>>"2x speed = 50 Elo point gain" equation. >> >>But "2x (2x ...(2x speed) ...)" is an exponential speed increase. *bonk* I'm an idiot. :) >That comment was probably too short. It was sufficient. :) >What I meant to say was the following: > >Any formula of the form "X times speed increase equals Y point rating gain" >actually specifies that you need exponential speed increase for linear >rating gain. But within this framework the rating gain per X times speed >increase does not diminish -- it rather remains constant at Y points. > >==> These are the formulas that specify "NO diminishing returns"! > >And your specific equation belongs to this class. What I _really_ meant to say was the following :): First, a postulate: Any increase in *search depth* will correlate to a ratings increase. I believe this to be a fairly linear curve. This will never give diminishing returns. Now, a corollary: Since the tree grows exponentially by a factor greater than two (I.e., the branching factor is higher than two, even with good pruning schemes.), eventually the speed/time needed to compute another ply will be prohibitive. This is where the speed->Elo equation will give diminishing returns. Even increasing speed exponentially by a factor of two, the size of the chess tree is growing faster. It gives diminishing returns because the processor speed will have to be *more than doubled* just to see any change in search depth. At each new ply of depth, processor speed will have to be increased even more just to see the gain. In effect, the speed increase will have to roughly match the tree-size increase to show *any return at all*, let alone simply diminishing ones. :)
This page took 0.01 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.