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Sac Chess. Game with 60 pieces. (10x10, Cells: 100) [All Comments] [Add Comment or Rating]
John Whelan wrote on Thu, Dec 17, 2015 01:14 AM UTC:
On consideration, it seems I must revise my position that the one-color only limitations of the Bishop seriously affect its value.

The Rook controls 14 squares on an empty 8x8 board.  The Bishop controls 13 at most (when in the center of the board) but more often only 7 (when at the sides).  The average for the whole board seems to be control of 8.75 squares, though in practice that number will be higher as players will tend to position their bishops to best advantage (i.e., they will tend to avoid sides and corners).

Divide both by a similar factor (2.8) and you get 5 for a Rook, and 3.125 for a Bishop (or perhaps higher in practice for the reasons stated), which is not too different from their relative values as found in practice.