Author: Andreas Stabel
Date: 07:54:38 06/29/00
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On June 29, 2000 at 09:11:47, Robert Hyatt wrote: >On June 29, 2000 at 08:16:25, Andreas Stabel wrote: > >>I have made a program that calculates this and here is the result to ply 7. >> >> | | Unique nodes | Unique nodes | Unique nodes | Factor | >>Ply| Total # nodes | ep = pawn two | ep = opposite| ep = Only if | prev. | >> | | | pawn can hit | ep is legal | row | >>---+---------------+---------------+--------------+---------------+--------| >> 0 | 1 | 1 | 1 | 1 | | >> 1 | 21 | 21 | 21 | 21 | 21.00 | >> 2 | 421 | 421 | 421 | 421 | 20.05 | >> 3 | 9323 | 8023 | 5783 | 5783 | 13.74 | >> 4 | 206604 | 109262 | 77796 | 77796 | 13.45 | >> 5 | 5072213 | 1351950 | 898812 | 898812 | 11.55 | >> 6 | 124132537 | 15334851 | 10281864 | 10281862 | 11.44 | >> 7 | 3320034397 | 160373323 | 106193912 | 106193643 | 10.33 | >> 8 | 88319013353 | | | | | >> 9 | 2527849247520 | | | | | >> >>It is interesting to note how great the reduction is just by not >>setting the E.P. target square if there is not pawn to hit. This simple >>test reduses the number of unique positions by a third ! > > >How is this happening? If no ep is possible, how can you get more nodes when >you set the ep target, even though no pawn can make the capture??? > Two positions will be different with and without the E.P. target square set because they will get different hash signatures. So if a chess program first searches one and then later in the search encounter the other it will have to search again because it will not realize that it is in fact functionally the same position. If you just chech each time a pawn is move two forward, if there exist a pawn of the oposite colour which may hit this pawn before you set the E.P. target square you will avoid this. > > >> >>It is also interresting to note how the "branching factor" of unique nodes >>gets smaller - from 21 to nearly 10 from ply 6 to ply 7. One wonders if >>it continues to grow smaller. I've calculated that the average branching >>factor (average number of legal moves in all positions) in a game is 31. >> >>My program can calculate even greater plys, but I need a machine with >>more than 10Gb of disc space and it will have to run for 2-3 weeks, so >>don't know when I will be able to do this. It would be interesting to >>check my numbers with others if anybody have calculated this. >> >>Regards >>Andreas Stabel
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