Linear Chess

In early March 2005, during a road trip, my colleague Matt Riggott and I were struggling to help pass the time. Without pen and paper we were at a lost to play even the simplest of games. We managed to derive a form of noughts and crosses (Tic-tac-toe), where we played mentally without the aid of paper. We did this by breaking a 3×3 board into a single 1×9 line. Then instead of saying something like “X top left corner” we could simply say “X1” all the way to “X9”. Therefore, three in a row would win (1,2,3—4,5,6—7,8,9), modulo 3 was a winner (1,4,7—2,5,8—3,6,9), and so were the diagonals (1,5,9—3,5,7). After several entertaining rounds, we got to thinking if it was possible to scale this linear system up to games with more squares than a 3×3 grid. Chess was the next obvious candidate. With an 8×8 grid and pieces that have various forms of movement, it was mathematically possible to convert to a linear form, but difficult to conceptualize.

Linear chess is played on a single line 64 squares long. Each chess piece retains the same rules of movement, but it is computed slightly differently in linear form. For instance, in standard chess, a bishop can move diagonally either direction. In linear chess, the bishop moves ±7 or ±9 up to 8 times in a direction to prevent it from “wrapping” around to the other side of a conventional board.

Our experiment was to determine if it would be easier to remember where all the pieces are located on a 1×64 grid rather than an 8×8 grid. In the end we are still not sure, our prior knowledge and experience of 8×8 chess has biased the results.

Example Linear Chess Match

As proof-of-concept and an art project I took the 1996 chess match between Gary Kasparov and Deep Blue and recreated it move by move as if were played in linear chess form. The chess pieces were replaced by bars of various widths. Each players’ move is mapped to its own line. Moves that created “check” are emphasized accordingly with a black border.

Viewing the game, each move next to each other vertically, creates an interesting look into how “active” or “inactive” a piece is on the board. By looking left to right on the poster, you can immediately see if a piece is moving or if it has stayed in the same position, forming an almost a solid line. It might be possible, after hundreds of these visualizations to see a pattern that might not be as obvious in the 8×8 grid form or through the individual descriptions of each move. You can see in this example of often the king needs to be moved for Deep Blue compared to Kasparov.

If there is or is not any merit or contribution to the chess community for the linear chess visualization, it certainly makes for an interesting barcode style art piece.

The posters is available for downloading, feel free to make prints. The concept of linear chess is freely available to anyone who wants to re-create other famous matches or their own games.

Download Poster PDF

linear.chess.poster.pdf (52.56 KB)

Future Work

There is a standard format for describing Chess matches, it is called PGN. In the future I would like to create a program that will take this format and automatically generate a linear chess representation.

There is also a ChessML, an XML format for chess, from that file with the help of XSLT, it is possible to generate an SVG visualization of a Chess match in linear form.

Last modified: October 11, 2009 17:10:59 UTC

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