Author: Robert Hyatt
Date: 13:07:11 05/16/01
Go up one level in this thread
On May 16, 2001 at 15:10:33, J. Wesley Cleveland wrote: >On May 16, 2001 at 14:07:18, Robert Hyatt wrote: > >>On May 16, 2001 at 13:05:13, J. Wesley Cleveland wrote: >> >>>On May 15, 2001 at 22:11:15, Robert Hyatt wrote: >>> >>>>On May 15, 2001 at 12:18:43, J. Wesley Cleveland wrote: >>>> >>>[snip] >>> >>>>>>First, how do you conclude 10^25? assuming alpha/beta and sqrt(N)? >>>>> >>>>>It is a classic alpha-beta search with a transposition table large enough to >>>>>hold *all* positions found in the search. I'm guessing at the number of >>>>>positions, but I feel that the same logic should hold, as only positions with >>>>>one side playing perfectly would be seen. >>>> >>>>I don't follow. We know that within the 50 move rule, the longest game that >>>>can be played is something over 10,000 plies. IE 50 moves, then a pawn push >>>>or capture, then 50 more, etc. Eventually you run out of pieces and it is a >>>>draw. But 38^10000 and 10^25 seem to have little in common. The alpha/beta >>>>algorithm is going to search about 38^50000 nodes to search that tree to max >>>>depth of 10,000. >>> >>>Look at it another way. The only positions that are visited by an alpha/beta >>>search (with perfect move ordering) are those where one side plays perfectly. >>>The question is what fraction of the total number of positions that is. >>> >> >>The precise formula is: >> >> N = W^floor(D/2) + W^ceil(D/2) for all D. floor means round down in integer >>math, ceil means round up. For the cases where D is even: >> >> N = 2 * W^(D/2) which is 2 * sqrt(minimax). >> >>If you assume that the total number of positions is roughly 2^168, then you >>get 2 * sqrt(2^168) or 2 * 2^84. Which is fairly close to the number of atoms >>in the universe. > >2^84 = 1.9*10^25 If these were atoms, it would be 32 moles, or about 1kg of >silicon. I discovered that I was having a small overflow problem on my calculator. It told me that 2^84 was roughly 10^81, which is wrong.
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.