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> <i>https://en.wikipedia.org/wiki/Princess_(chess)#Value</i> <p> And guess who wrote that there! :-) <p> Note that arguments based on move counting on an empty board are often unreliable. Distant slider moves contribute very little to value, because during most of the game you will not be able to make them anyway due to blocking or board edges. And once the board population has dropped to where you can, they often lead to places where you have no business going anyway. In defending KRPKR it hardly matters how far away you can move the Rook from where the Pawn is. <p> The value of a piece is mostly determined by how efficiently a piece supports and combats Pawns in the end-game. <p> Another factor could be 'winning power' in often occurring Pawnless end-games, which determine how easily you can draw by acrificing a piece for the opponent's last Pawn to stop its promotion. E.g. Queen + minor (B or N) vs Queen is draw, making Q+minor+Pawn vs Q+minor also easy to draw. But Q+minor vs Chanchellor or Archbishop is a win. Q vs R is virtually always won, giving Q+P vs 2R a big advantage, but C vs R is only won if your King is not confined to its own board half by the Rook, and A vs R is a dead draw, making A+P vs 2R a hopeless proposition. More or less coincidental properties like that might have impact on the value, although it is different to separate cause from consequence here:one could also argue that some pieces win and others not against a given opposition is because they were generally inferior. That it is not possible to checkmate a bare King with a pair of Knights, but you can do it with a pair of Phoenixes, does not seem to be tracable to general inferiority of the Knight, however. (E.g. KRKN is generally a draw, but Rook vs Phoenix is a general win.)