Playing Chess Against Its Mirror Image
When we observe the initial arrangement of pieces on a standard chessboard we find that the setup was designed in a way that a player is initially facing his proper mirror image (put a mirror perpendicular to the frontier line between white and black). Now suppose that white plays a simple game against his mirror image which has black pieces. Then we have:
1. e2-e4 e7-e5 2. Ng1-f3 Ng8-f6 3. Bf1-c4 Bf8-c5 4. d2-d3 d7-d6 5. Nf3-g5 Nf6-g4 6. Bc4xf7+
But at this point, the mirror image cannot make the symmetrical move; that is playing Bc5xf2+, because black King is already in check and he must move either to e7 or f8. So the symmetrical play between white and its mirror image is broken at the 6th move.
Now is it possible to correct this so that the play will continue until white or its mirror will win the game? The only possible way to do so, is that a piece in front of the King diagonally, horizontally or vertically does not check the King (eg. Bf4xf7 is not a check to the Ke8). Also in the case of two queens facing each other horizontally, vertically or diagonally no queen can capture its facing Queen. This also will apply to the Rook, Bishop and Knight. Of course, we already know that a pawn facing another pawn cannot capture it. We can simply allow that a piece can only capture another distinct piece. With these new rules, is it possible that white or its mirror will win the game? In other words, can the symmetrical play between two players lead to a win for one or the other? To see this, let's consider the previous game with the new rules.
1. e2-e4 e7-e5 2. Ng1-f3 Ng8-f6 3. Bf1-c4 Bf8-c5 4. d2-d4 d7-d5 5. Nf3-g5 Nf6-g4 6. Bc4xf7 Bc5xf2 7. Ke1-f1 Ke8-f8 8. Nb1-c3 Nb8-c6 9. Be7-d5 Be2-d4 10. Bd5xKc6 Bd4xKc3 11. Bc6-d5 Bc3-d4 12. h2-h3 h7-h6 13. h3xNg4 h6xNg5 14. Qd1-f3 Qd8-f6 15. Bc1xg5 Bc8xg4 16. Qf3xBc4 Qf6xBc5
(Check is not allowed with the new rule. Also a Queen facing the King cannot capture it.)
17. c2-c3 c7-c6 18. Bd5-b3 Bd4-b6 19. d3-d4 d6-d5 20. e4xd5 e5xd4 21. d5xc6 d4xc3 22. Ra1-d1 Ra8-d8 23. b2xc3 b7xc6 24. a2-a4 a7-a5 25. c3-c4 c6-c5 26. Rd1-d5 Rd8-c4 27. Qg4-c8 Qg5-c1 28. Qc8-b7 Qc1-b2 29. Qb7xBb6 Qd2xBb3 etc...
Without going further, the game must end with a draw between a player and its mirror image. In other words, a symmetrical play between two chess players cannot end in favor of one or the other, if one adopts the aforementioned new rules.
[Editor's note: if check is not allowed, then checkmate is not possible and it seems that the conditions for winning must be modified. But modified winning conditions are not specified here. -DH]
[Comment: Play for black seems completely deterministic. It might be more interesting for white to start the game with one move, then have both white and black make two moves each turn, the first mirroring the opponent's last move, the second a "free will" move. -DH]
Written by A. Missoum. Edited by David Howe.
WWW page created: August 18, 1997. Last modified: March 9, 1999.