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Jeremy Lennert wrote on 2012-09-29 UTC
I don't think that's true about the bishops' value, David.  In addition to being color-bound, bishops also suffer a significant loss in mobility near the edges and corners of the board, while rooks suffer much less--due to the fact that the board edges line up with the rooks' moves.  (There are also several other strategic differences of uncertain importance, such as the fact that the rook can interdict the movement of the enemy king, and the differing ways each of them interact with pawns.)

In fact, I would guess that this loss of mobility is far more important than colorboundness, because players of cylindrical chess (where bishops do not lose mobility at the sides of the board) have reported bishops to be roughly the equal of rooks--despite still being colorbound.

It wouldn't surprise me if BK and RK are closer in value than B and R, though at a quick guess I'd expect RK would still be noticeably stronger.

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