Color Flipping
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Color Flipping a chess position refers to the vertical flipping or mirroring of all pieces along the horizontal axis between the 4th and 5th rank also swapping the color of the flipped pieces from White to Black and vice versa, the side to move, the castling rights and the rank of a possible en passant target square from six to three or vice versa accordantly. The resulting position is mirror equivalent, pawn and pieces have the same span length or home rank relation. A white pawn on the light square c2 becomes a black pawn on the dark square c7. Color flipping a vertical symmetrical or mirror position (same castling rights, no en passant possible) results in the same position as if the side to move performed a null move:
Contents
Sample
| Giuoco Piano | Giuoco Piano Symmetrical | ||
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| r1bqk1nr/pppp1ppp/2n5/2b1p3/2B1P3/5N2/PPPP1PPP/RNBQK2R w KQkq - | r1bqk2r/pppp1ppp/2n2n2/2b1p3/2B1P3/2N2N2/PPPP1PPP/R1BQK2R w KQkq - | ||
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| rnbqk2r/pppp1ppp/5n2/2b1p3/2B1P3/2N5/PPPP1PPP/R1BQK1NR b KQkq - | r1bqk2r/pppp1ppp/2n2n2/2b1p3/2B1P3/2N2N2/PPPP1PPP/R1BQK2R b KQkq - |
Book Transpositions
During the opening, in some lines, White may intentionally lose a tempo, to transpose into a color flipped position of an opening White likes to play the "Black" side, which might be considered in chess programs book access code, see for instance WMCCC 1988, Pandix-Y!88.
Flipping an 8x8 Board
An 8x8 Board with a rank-file mapping, needs to perform an exclusive or with 56 (A8 in LERF) to vertically flip square coordinates. Assuming piece color is least significant bit and empty square is zero, a pure 8x8 Board may be color flipped that way in C:
int board[64], sq, s, f;
for (sq = 0; sq < 32; ++sq) {
s = board[sq];
f = board[sq^56];
board[sq] = f ^ (f != 0);
board[sq^56] = s ^ (s != 0);
}
Looking for Bugs
A side to move relative, bug free static evaluation should have the same score for both positions. Search is a different issue, since move ordering might be slightly different for instance in bitboard programs due to different order in bitboard serialization if one doesn't use a symmetrical bitscan by side to move. Similar to the butterfly effect in chaos theory a minor initial difference might amplify to enormous effects during the search. However, if the search behavior of a tactical test position of a most deterministic chess engine (e.g. no parallel search), varies by magnitudes in solution depth and time between original and color flipped position, one may take a closer look performing some logging and/or debugging.
Monochrome
An idea to unify and simplify move generation and to get rid of order dependencies, is to perform a color flip of the position and its internal board representation directly after making a move, to make the engine white to move only, that is only generating white moves, or similar, to keep a normal and flipped board to update them incrementally.
MicroChess
Jennings' approach with MicroChess was similar [1], but instead of vertical flipping (xor 56) he reversed or rotated the board by 180 degrees (xor 63), like players changing places and looking the board alternately from White's or Black's point of view, with some considerations of the additional horizontal mirroring, concerning castling and en passant.
Quad-Bitboards
Gerd Isenberg proposed a make move - color flipping approach using Quad-Bitboards [2] . The black Zobrist keys were the byte-swapped white Zobrist keys from the vertically flipped squares (xor 56). In symmetrical positions this gains some additional hits while probing the transposition table. But symmetrical mirror positions, or symmetrical subsets have the property, their xored hashkey has only 32 distinct bits since hashkey equals flipVertical(hashkey), for instance:
01020304|50607080 // white pieces ^ 80706050|04030201 // black pieces of a mirror position = 81726354|54637281
Six-Two Bitboards
The common six piece kind and two color bitboard board representation takes eight byte swaps to color flip the whole board.
Keeping two Boards
Rather than flipping the board after each make, Reinhard Scharnagl proposed monochrome move generation by keeping a normal and a color flipped board, both incremental updated [3] . He further suggested asymmetrical piece coding with less piece codes (only one or two) for the pieces of the side not to move. His approach has also the advantage to keep independent Zobrist keys for all squares and pieces.
See also
- Color
- Diagonal Mirroring
- Flipping, Mirroring and Rotating of Bitboards
- Horizontal Mirroring
- Side to move
- Vertical Flipping
Publications
- Fernand Gobet (1993). A Computer Model of Chess Memory. Proceedings of the 15th Annual Meeting of the Cognitive Science Society, pp. 463-468.
Forum Posts
- Conversion to dual positions for EPD testsuites? by Leen Ammeraal, CCC, November 26, 2001
- fen to fen functions by Uri Blass, CCC, May 21, 2007
- Comparison data of Crafty vs Rybka that I promised 2 days ago by Les, CCC, June 01, 2007
- color-flipped perft by Gerd Isenberg, November 04, 2007
- Board without color flags by Fritz Reul, CCC, October 31, 2009
- Position flipping by Steven Edwards, CCC, August 05, 2013
- Black/White symmetry in move generation by Jeffery A Esposito, CCC, November 25, 2014 » Move Generation
- Symmetric move generation using bitboards by Lasse Hansen, CCC, December 20, 2014
- reversed-color transpositions by John Fishburn, CCC, March 11, 2016
- FEN - Flipper for Windows by Matthias Gemuh, CCC, May 17, 2017 » FEN, EPD
External Links
References
- ↑ Peter Jennings (1976). MicroChess, a Chess playing program for the 6502 Microcomputer. pdf, Courtesy of Peter Jennings, The Computer History Museum
- ↑ color-flipped perft by Gerd Isenberg, November 04, 2007
- ↑ Computerschach mit monochromen Methoden ? by Reinhard Scharnagl, OpenChess - Deutsches Forum, January 27, 2011 (German)
