Interesting question. I couldn't find anything about this online, and I don't really have a clear answer but I suspect rotational symmetry might slightly increase the chance of handing White a significant advantage. For example, I looked briefly at a starting position with queens on h1 and a8 (and bishops g1/b8) and then 1.g3 or g4 may make life a touch awkward for Black.
Having said that, I've played about 20 slow and serious games of 'Double Fischer Random' (same as Chess960 but the players have separate randomisations) and I've generally found that the stronger player wins out regardless. Nearly all those games were played in pairs, so that the same starting position was used with both white and black against a particular opponent. The rotational symmetry idea would of course be a small subset of DFR.
Chess960: Why Mirror Symmetry, Not Rotational Symmetry?
After some stockfish analysis I've observed that the computer evaluation is always negative in rotational symmetry starting positions. This is really interesting because is mostly best for White to have a symmetrical position, but it doesn't though make sense why Black has advantage when White has the advantage of the next move.
So, maybe they just wouldn't like White to be on weaker position since the game would be so much different. The games with rotatiolnal symmetry do however look more interesting (maybe partly because basic opening theory doesn't work on these games which makes them look different). By the way, chess's starting position was rotational symmetric in the 7th century. I don't know when it was changed.
After some stockfish analysis I've observed that the computer evaluation is always negative in rotational symmetry starting positions. This is really interesting because is mostly best for White to have a symmetrical position, but it doesn't though make sense why Black has advantage when White has the advantage of the next move.
I did some testing myself and I wonder if you made the same mistake I made and did not make the castling rights equal. I was always flipping the White pieces, which took away their castling rights, and gave Black the advantage. Once I turned off Black's castling rights, the evaluation tended to give White the advantage.
After some stockfish analysis I've observed that the computer evaluation is always negative in rotational symmetry starting positions. This is really interesting because is mostly best for White to have a symmetrical position, but it doesn't though make sense why Black has advantage when White has the advantage of the next move.
I did some testing myself and I wonder if you made the same mistake I made and did not make the castling rights equal. I was always flipping the White pieces, which took away their castling rights, and gave Black the advantage. Once I turned off Black's castling rights, the evaluation tended to give White the advantage.
Yeah, not sure about stockfish but alpha zero valued castling rights at about 1 to 1,5 pawns in extensive self-play. Also, certain rotationally symmetrical ideas seem to be more powerful when you're up on tempo. Rooks in vanilla starting chess position are relatively weaker than minor pieces until developed to a half open or open file, or applying pressure in the center. If you swap queen and rook, and move kings in a rotationally symmetrical fashion, so that the rook and the pawn backed by it opposes the opponent's king and his pawn in the center, stockfish says it's already about +0,7 for white, as opposed to the 0,2 in rotational symmetrical when it's just the king and queen swapped.
I’m a relative newcomer to chess, and brand new to Chess960. I love the idea of Chess960 (though, to be clear, I am still very bad at ALL Chess variants), because it throws out established and memorizable openings and theories, and forces players to think on their feet using more general guiding principles and predictive foresight. But I’m curious: is there a reason Black’s back rank is organized to mirror White’s, rather than to make the board rotationally symmetric?
As I understand it, Chess960 begins with the White producing a randomized 1st rank using every piece except the pawns (subject to the restrictions that make Chess960 Chess960), and then black places its material in the 8th rank in the same files as white.
However, one could easily also arrange Black’s pieces such that they are the same as White’s if the board is rotated 180degrees - i.e. if white places a rook on b1, black places a rook on g8, if white places a queen on c1, black places a queen on f8, &c. This has the advantage that the board looks exactly the same in terms of player’s material placement relative to their opponent’s, with the only difference being turn order.
I recognize that Chess is also organized by mirror symmetry (the “Queen to her color” rule), but I presumed this was mostly as a historical rule, since in Chess the rest of the back rank material placement has both rotational and mirror symmetry, but due to the asymmetry of the king-queen pair one of thise symmetries must be broken and rotational symmetry lost that historical coin toss.
TLDR: So, arriving at my question, is there a reason, either heuristic or firmly rooted in theory, that Chess960 opted for mirror symmetry over rotational symmetry, either to make the game more fair or more interesting? Or is it just imitating the (presumed historical?) mirror symmetry of regular chess?
My only two thoughts on the strategic differences are 1) mirror play makes it so that if Black mirrors White’s pawn moves, Black opens the development of the same back rank material as White while simultaneously stopping pawn advancement, which may make countering white’s opening play more easy since you may halt pawn advancement and develop similar material at the same time, and 2) it may be good to have straight moving pieces (rooks and, in particular, the Queen) in the same file so that they may more easily be used to counter each other in early and middle gameplay.