Author: Uri Blass
Date: 14:10:53 10/03/01
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On October 03, 2001 at 16:19:41, Dann Corbit wrote: >Here is Michael Langeveld's calculation: >Ply(0) Nodes= 1 >Ply(1) Nodes= 20 = 20,00x ply(0) >Ply(2) Nodes= 400 = 20,00x ply(1) >Ply(3) Nodes= 8902 = 22,26x ply(2) >Ply(4) Nodes= 197281 = 22,16x ply(3) >Ply(5) Nodes= 4865609 = 24,66x ply(4) >Ply(6) Nodes= 119060324 = 24,47x ply(5) >Ply(7) Nodes= 3195901860 = 26,84x ply(6) >Ply(8) Nodes= 84998978956 = 26,60x ply(7) >Ply(9) Nodes= 2439530234167 = 28,70x ply(8) How much time did his program need to calculate the number for 9 plies? It is possible to save search time by the following trick: If you remember all the possible positions after 5 plies and the number of games that lead to that position then you need only to calculate a sum of a lot of a*b numbers. Example the position after 1.e4 e5 2.d4 d5 3.c4 can happen in exactly 12 games(white has 6 possibilities to change order of moves and black has 2 possibilities to change order of moves) It means that you can calculate 1999328*12 for that position when 1999328 is the number of possible 4 plies game after 1.e4 e5 2.d4 d5 3.c4 Maybe it is even better to remember all the possible positions after 6 plies and there are cases when there are hundreds of games to get the same position after 6 plies Example: 1.e4 e5 2.Ba6 Ne7 3.Bf1 Ng8 leads to the same game as 1.e4 e5 2.Qh5 Qh4 3.Qd1 Qd8 and as 1.Nf3 e5 2.e4 Nf6 3.Ng1 Ng8. I can see easily that after 1.e4 e5 white has: 1)4 possibilities to move the queen 2)5 possibilities to move the bishop 3)5 possibilities to move the knight It is 14 options of playing and going back. Black has also 14 possibilities to play and go back so you get 14*14=196 games when both sides start with 1.e4 e5 and get this position after 6 plies. There are also cases when they do not start in this way like 1.knight move e5 2.e4 piece move 3.knight go back,piece go back Uri
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