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David Paulowich wrote on Sat, May 3, 2008 12:22 AM UTC:

Reinhard Scharnagl discussed the handicap of one side having a powerful chess piece without exchangeable counterparts in the Piece Values thread [2008-05-02]. This thread is devoted to testing Archbishop versus Rook and Knight on an 8x8 board, while trying to avoid such problems. Opinions expressed here on the value of the Archbishop vary from a pawn less to a pawn more than the combined value of the Rook and Knight.

First, replace both Queens with Archbishops. Keep Black as rnbakbnr and change White to -ABAKBNR, by removing the Rook from (a1) and replacing the Knight on (b1) with an Archbishop. Now both sides will have opportunities to exchange pieces for identical counterparts.