Author: Eugene Nalimov
Date: 10:23:26 10/13/98
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Using my indexing schema, you'll get smaller tables. Main improvement is that I don't allow enemies pieces to occupy some squares where they will check king of the side not on move. Of course it's not possible to easily forbid all those squares, but you can more-or-less easily forbid squares near the king. Largest savings are, of course, for tables with queens or knights; smallest - for tables with pawns and bishops. Worst case for such schema is KRBKP, if I remember it correctly. Count of positions in 2 tables (one for white and one for black to move) is 598,093,440 - compared to 655,708,032 when using Ernst's simpler and faster schema, and 1,073,741,824 when exploiting only one symmetry. Eugene On October 13, 1998 at 13:04:17, Ernst A. Heinz wrote: >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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