From: "Dr. Rainer Staudte" To: Multiple recipients of list CHESS-L The 72 years old David Bronstein, at Advances in Computer Chess (8), Maastricht, June 27, 1996: "For me it is easy: Rook=5, Bishop=4, Knight=3." When you have seen how Bronstein attacks playing against a computer you will understand why his bishop has such a strength.In the ordinary world of FIDE chess, some players like their Bishops and use them especially well, while other players are skilled at positions where one side has two minor pieces and the other side has a Rook.
Even when two players are of equal strength, one player's Knights may (in effect) be stronger than the other's.
The reason why one player likes her Rooks and uses them better is because she has spent more time thinking about how best to use them, and of course this effect has been reinforced by the pleasant experience of winning games with great Rook play, and she learned more about Rooks from those games, and ... it is a cycle that builds upon itself.
In Chess with Different Armies, there are more different kinds of pieces, so there will be more personal variation between players.