Author: Timothy J. Frohlick
Date: 23:54:31 01/12/00
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On January 12, 2000 at 18:34:49, Dan Ellwein wrote: >Hi > >Just wanted to bounce this off of the group and see if this is an accurate >representation of how many (non redundant) pawn positions there are in chess... > > >(0,8)(1,7)(2,6)(3,5)(4,4) 8P 48x47x46x45x44x43x42x41 x5 = _______ >(0,7)(1,6)(2,5)(3,4) 7P 48X47X46X45X44X43X42 x4 = _______ >(0,6)(1,5)(2,4)(3,3) 6p 48X47X46X45X44X43 x4 = _______ >(0,5)(1,4)(2,3) 5P 48x47x46x45x44 x3 = _______ >(0,4)(1,3)(2,2) 4P 48x47x46x45 x3 = _______ >(0,3)(1,2) 3P 48x47x46 x2 = _______ >(0,2)(1,1) 2P 48x47 x2 = _______ >(0,1) 1P 48 x1 = _______ > > >Number of non redundant pawn postions in chess -- TOTAL: _______ > >haven't done the math on it yet, but it looks like about 75 trillion... > >thanks... > >PilgrimDan Dan, I don't think the "a" pawn is going to end up on the e,f,g,or h files and don't forget that the black pawns prevent occupation except by capture of the white pawns. You also have to account for en passant which usually occurs only once per game at most. [D] 8/pppppppp/8/8/8/8/PPPPPPPP/8 So the progression should be 20x19x18....etc and be extended out for a total of sixteen pawns. 20x19x18x17x16x15x14x13x12x11x10x9x8x7x6x5x4= 8.109673360589e+17 which is a pretty big number of possibilities. Even if we limited the combos to (Whitemoves x 10x9x8x7x6x5x4x3) + (Blackmoves x 10x9x8x7x6x5x4x3)=3,628,800 possibilities you can see that we will not run out of moves soon. If the average game is 75 moves or 150 ply we would have to play at least 24,192 games to exhaust the possibilities. Again, since not every move is a pawn move we would have a variable number of pawn moves and positions. So if only one quarter of our moves are pawn moves we would have to play about 100,000 games to come to a correct estimation of the number of different pawn structures. This is just my opinion and is probably wrong. Tim Frohlick
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