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Check out Chess with Different Armies, our featured variant for July, 2024.
Check out Chess with Different Armies, our featured variant for July, 2024.
A Queen is 9 because piece values are relative quantities, and you need to define a scale by assigning some, otherwise arbitrary value to one reference piece. Often one chooses Q=9 for that. (One could also define Pawn=1, but Pawns are very cooperative pieces, and their value changes very much depending on neighboring friendly and enemy Pawns, so they are not really suitable as standard.)
With that calibration B=N=3 (on 8x8), because a material imbalance where one player has a Bishop and the other a Knight on average give both players equal chance, just like an imbalance of 2N+B vs Q, as has been established by centuries of play.
The Archbishop has value 8.25 because with an imbalance of A+P vs Q it wins more often than not, but with pure A vs Q the Q has about a 3 times larger advantage (in the win vs loss statistics).