# Symmetries in chess

The same games of chess could be played if:

• white and black squares were swapped (i.e. the board rotated by 90 degrees)

or

• king and queen were swapped in the starting position (i.e. white/black kings on d1/d8 and white/black queen on e1/e8)

or

• black was allowed to start the game

Are there any other transformations, which leave the game the same (I think not)?

What is the origin of the current board orientation and king/queen position and first move for white?

Has anybody studied the effect of such transformation on the play? For instance:

• How much worse would an experienced player play?
• Would there be a preference for different kind of openings or trading pieces differently? For instance I could imagine that if the board was rotated 90 degrees (change of square color) this could change play because say a black bishop on a dark square has different contrast than a black bishop on a light square. Similarly, if king and queen were swapped, this could affect play as people are right or left handed.
• Combinations of the three elementary symmetry transforms also count. And there is "Bystander Chess" or "Kiebitz Chess" which is played "from the side" on a Chessboard roteted 90 degrees with the pawns marching horizontally. Nov 16, 2016 at 14:52
• Good point. I did not know about "Kiebitz Chess". Nov 16, 2016 at 15:05
• Are there any other transformations, which leave the game the same. No, there aren't. Another observation: when playing blindfold chess, I do not 'see' a board with black and white squares. This might be different for other people, though. Nov 16, 2016 at 21:30
• By the way, I believe that "white moves first" and "white on the right" were codified fairly recently in the history of chess, i.e., sometime in the 19th century. Not sure about the positions of the K and Q.
– bof
Aug 3, 2017 at 17:59
• Here's a rather confusing transformation I saw played in a chess club: one player uses white pieces and black pawns, the other uses black pieces and white pawns.
– bof
Aug 3, 2017 at 18:01

The only symmetries that leave the game unchanged are rotations, reflections and central inversion.

There are 2 reflections (vertical being swapping king and queen, horizontal being black moves first) and 4 non-trivial rotations (90, 180, 270 and 360 degrees). Doing nothing (i.e. a rotation of 0) is the group theory identity element.

The board can also be centrally inverted. Think of having a double sided board that you flip over. So a1 becomes h8, a8 becomes h1 etc.

If you are interested in studying symmetry in a mathematical context, please investigate group theory.

Bad_Bishop forgot the third reflection, if the board was upside-down, the game would remain the same..

In the beginning, there was only a grid, no colored squares. The blackening of alternating squares was probably introduced to help see the legal diagonal movements.

The story I heard for first move was giving white the first-move advantage as black was thought to be a lucky color at the time. I assume black and white were used at they were the easiest colors to produce.

As a fairly strong player, altering the color(s) or flipping horizontally would make no difference. Although having a neon set would bother me, but not alter my chess ability. Another problem is a great variance in the piece shape. You can't just make the queen look like (that girl from Avatar) and expect me to treat her like that piece. Just to exaggerate this point, switch the king and queen pieces and see how many times you revert them back to their originals.