Can Black Force a Win?

It is commonly believed that, with correct play, White can force at least a draw from the game's initial position. In the hope of one day seeing a (computer-aided) proof, we assume the role of the devil's advocate and ask whether White might be in zugzwang and hence Black might have a forced win in the game's initial position. For curiosity, we provide two examples below of symmetrical and legal positions in which White is in zugzwang and Black can force a win. Let us define a position on a chess-board to be symmetrical if the following conditions (i)-(v) hold: (i) the configuration of the pieces is symmetrical, i.e., moving pieces from their current squares to the square(s) obtained by a reflection about the line (the "4.5th" rank) along the middle of the board, and then changing the colours of all pieces (Black to White and White to Black) restores the pieces to their original configuration*; (ii) either both Kings are eligible to castle Kingside (possibly later on) or neither King is; (iii) either both Kings are eligible to castle Queenside (possibly later on) or neither King is; (iv) no Pawn can be captured "en passant"; (v) it is White's move. We further say that a position is symmetrical and legal if it is both symmetrical and (vi) it can be obtained from the initial position via some legal sequence of moves. (Note that the sequence of moves need not follow symmetrical play). It follows from (i) and (vi) that neither King is currently in check. Diagrams 1 and 2 below are both examples of symmetrical and legal positions from which Black has a forced win. The position in Diagram 1 below can be reached from the initial position by the following sequence of 21 moves: 1. e4 e5 2. d4 d5 3. dxe5 dxe4 4. Qd5 b5 5. Qxa8 Qd4 6. b4 Qxal 7. h4 h5 8. Bf4 Bf5 9. Bh2 Bh7 10. Be2 Be7 11. Bg4 Bg5 12. Nf3 Nf6 13. g3 g6 14. Kfl Qxbl+ 15. Kg2 Qgl+ 16. Bxgl Kf8 17. Qxb8+ Kg7 18. Qg8+ Bxg8 19. Kh2 Kh7 20. hxg5 hxg4 21. exf6 exf3 Note that giving White a Rook at g2 and Black a Rook at g7 in Diagram 1 leaves the position legal and symmetrical, and White is still in zugzwang. Note further that the above comments all still apply if we replace the white Rook at hI and the black Rook at h8 respectively by a white Knight and a black Knight.