It reminded me of a study I did to be able to visualize how a knight moves. I put a zero in the middle of a spreadsheet, and placed formulas to increment by one in all the square the knight could go to in one move. Then, around those squares, I incremented again, to find all the squares a knight could go in two moves. I did this out to 9 moves.
I decided just seeing the numbers wasn't enough, so I wrote a script to color the spreadsheet. Here is the end result. The pattern reminds me of something your grandmother would cross stitch.
2 comments:
I would restrict the analysis to the standard 8x8 chessboard. There are interesting patterns to be observed on the chessboard about how piece movement options vary by its location on the board. On a clear chess board, the knight has 8 possible moves in the center of the board, but only two if it's in a corner. A bishop can reach 13 squares from the center, but only 7 from a corner. Although this seems to make the bishop much more powerful than a knight, the bishop's potentiality is limited by the fact that it can never touch half of the squares on the board. A rook can reach 14 squares from any position. A queen can reach (bishop plus rook) 21 squares from a corner and 27 squares from the center. If one counts the number of possible squares accessible by each piece, from each of the squares that piece can potentially reach, one finds that the ratio of these numbers to each other roughly duplicates the point "value" assigned to the pieces. For example, the 5-point rook can always reach 14 squares from any position, while the 9-point queen averages just less than double that amount. The traditional "point value" seems to be correlated with piece mobility, and piece mobility appears to be calculable in a way that could contribute to our ability to estimate the value of "position vs. material" in different positions (e.g. pawn structures, exchange sacrifices, etc.) Your technique seems to be very applicable to this sort of analysis, except that some means would eventually have to be found to estimate, for example, the changing movement/position probabilities under actual game conditions (e.g. a completely closed pawn structure that reduces the value of the bishops, and often the other pieces as well).
Mike S.
Wildly creative, Chris! I also logged your Blog Thumbprint blog entry.
Post a Comment