Author: Graham Laight
Date: 05:19:03 05/10/01
Go up one level in this thread
On May 10, 2001 at 08:14:26, Graham Laight wrote: >On May 10, 2001 at 08:01:16, Graham Laight wrote: > >>On May 10, 2001 at 05:46:24, Jesper Antonsson wrote: >>>Great, then, hopefully, this is *the* point where we disagree. Now, the 3-fold >>>repetition rule and 50-move rule are not mandatory, but they are there. How do >>>you handle these positions in the search in Crafty (your "algorithm")? I would >>>assume that you label them a draw and search no deeper. Perhaps you do not >>>always *claim* the draw when such a position is at the root, but, as I said, you >>>probably treat them as draws in the search. This is because mini-max "assumes" >>>best play from both sides, and either the position is a draw whether 3/50 rules >>>are used or not, in which case it is safe to return draw-score, or the player >>>that is losing, using "best play", should claim the draw, in which case minimax >>>should also return a draw score. >>> >>>So, from a search perspective, or solving-chess-perspective, we should treat >>>these positions as draws, and when we do, a "good" chess algorithm in theory >>>stops it's exponential behaviour at a certain depth. >> >> >>Given the application of the 50 move rule, one can easily estimate an absolute >>limit to the number of possible chess games. >> >>Number of pieces which can be taken: 30 >>Number of possible pawn pushes: 6 * 16 = 96 >>Total number of 50 move rule avoidence events: 96 + 30 = 126 >>Maximum possible number of moves: 126 * 49 = 6,174 >>Maximum possible number of plies: 6,174 * 2 = 12,348 > >This also allows us to estimate when chess will be fully solved (all possible >chess games generated). > >Max possible plies in a chess game: 12,348 >Number of years per increase of 1 in search ply depth: 3 (just a guess, I admit) >Number of years to wait: 3 * 12,348 = 37,044 >Actual year: 37,044 - 2001 = 35,043 Oops - bit of brain fade there! Should of course be: 37,044 + 2001 = 39,045 Allowing for the progress already made, that makes it about year 39 thousand. -g >This is, of course, assuming that Moore's law continues to hold (which is not a >safe assumption based on only 35 years of history). > >-g > >>Average number of possible moves per position: 37 (you could work with a maximum >>possible if you prefer) >>Maximum possible number of games: 37 ^ 12,248 >>= 1.4 e+19,364 >> >>-g
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.