I have seen several books that presented the most primitive possible attempt at providing a mathematical foundation for the values of the chess pieces. In this method, you simply slap a piece down in the center of an empty board, and count how many squares it can move to. The results of this clumsy attempt will be shown in the MAX column the next time the table of values is repeated.
In one 19th-century book, however, I saw a better attempt made; in that book, the author repeated the process for every square on the board, and then calculated the average mobility. (Details available!)
This is the absolutely correct way to calculate the Knight's mobility, and since a piece's mobility must be an important part of its value, this method is definitely an advance beyond the most primitive methods.
In the following table, all values have been translated so that the Knight has the same value (5.25) in every column:
PIECE STAND SPIEL PROG MAX AVERAGE HANDBUCH ====== ===== ===== ==== ===== ======= ======== Pawn 1.75 1.75 1.59 ? ?.? 1.49 Knight 5.25 5.25 5.25 5.25 5.25 5.25 Bishop 5.25 5.25 5.25 8.53 8.75 5.26 Rook 8.75 7.88 7.95 9.19 14.00 8.52 Queen 15.75 14.88 15.11 17.72 22.75 15.35 King 7.00 6.56 5.25 6.56 Ferz 3 2.63 3.06 Alfil 2 2.63 2.25 Wazir 2.63 3.50 Dabbaba 2.63 3.00 KnightRider 7.88 9.50 Chancellor 14.44 19.25You will notice that several new pieces and new columns have been added to the list. Need an explanation?
The most important new thing in this table is the AVERAGE column, which gives the results for average mobility, using the method discussed in this section. Its results seem to be fairly accurate for the short-range pieces, but not for long-range pieces such as the Bishop, Rooks, or Queen.
People have thought about the values of chess pieces before, but they never thought very hard or long.