Author: Robert Hyatt
Date: 09:57:40 02/05/03
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On February 05, 2003 at 06:01:16, Marc Bourzutschky wrote: >On February 05, 2003 at 04:25:46, GuyHaworth wrote: > >> >>Maybe they differ because an a1-h8 rotation does not leave the position >>unchanged when there are Pawns on the board. >> >>So ... they wouldn't be the same even if there was no e.p. rule. >> >>g > >The position does not have to be unchanged, only a 1-1 mapping needs to exist. >The symmetry actually used is: > >1. Flip the colors of all pieces >2. Flip the board (a1 <-> a8, h1 <-> h8, etc) including e.p. square >3. Change side to move > >For KPKP all positions in .nbb can be mapped to a position in .nbw this way, so >.nbb and .nbw have the same information content. There must be another reason >why Eugene keeps both files, probably more a convenience than anything else. >This will get more interesting once he generates KRPKRP, etc. Note that probing >code needs to be aware of the above transformation even for non-symmetrical >endings because, e.g., endings such as KPKBP.NBW have to get mapped to KBPKP.NBB >(including potential e.p. squares). > >-Marc Are you considering the 10 squares the king is constrained to occupy? I'm not sure how the symmetry will work since there is now a diagonal reflection that must be done, and that would leave pawns moving sideways... If I understand what you are asking, that is...
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