Author: Ernst A. Heinz
Date: 10:04:17 10/13/98
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On October 13, 1998 at 12:23:29, John Coffey wrote: > >How many possible positions are there in all 4 or 5 piece endgames? >I am thinking that it must be between billions and trillions. >do such endgames take advantage of symetry? If you do not discount illegal positions there are 64^X possible constellations of X pieces. By removing symmetries, not placing more than one piece on the same square, and not placing the Kings directly beside each other, you can easily reduce this number to: (a) 462 * 62 * 61 for 4-piece endgames without Pawns, (b) 3612 * 24 * 62 for 4-piece endgames with a single Pawn, (c) 3612 * 24 * 47 for 4-piece endgames with 2 Pawns (no en-passant), (d) 462 * 62 * 61 * 60 for 5-piece endgames without Pawns, (e) 3612 * 24 * 62 * 61 for 5-piece endgames with a single Pawn, (f) 3612 * 24 * 47 * 62 for 5-piece endgames with 2 Pawns (no en-passant), (g) 3612 * 24 * 47 * 46 for 5-piece endgames with 3 Pawns (no en-passant). I have submitted an article to the ICCA Journal which describes the according index schemes among other things. =Ernst=
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