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John Whelan wrote on Wed, Dec 16, 2015 11:22 PM UTC:
I don't think one can be too dogmatic about the relative value of pieces across all contexts.

It is very useful in Chess to throw lesser pieces onto the front lines for profitable exchanges, while using the Big Guns for backup.  Whether a Big Gun is worth more to you than 2 lesser value pieces will probably depend on the balance between Big Guns and lesser pieces that you already have.

But I think that generally, a singe piece that combines the powers of two lesser pieces would be worth less than those two pieces.  As evidence of this, I offer the fact that a Queen controls twice as many squares as a Rook (and as many squares as 2 Rooks), but is worth less than two Rooks.

A Bishop has the same firepower as a Rook, in terms of the number of squares it controls.  The reason a Bishop is worth less than a Rook is that a Bishop is confined to half the board, and the Rook is not.  A Queen gains the Bishop's extra firepower without suffering from its limitations.  This is the reason why a Queen is generally worth more than a Rook and Bishop combined.

This logic does not apply to the Amazon.  Neither the Knight nor the Queen is limited in the way the Bishop is; so a piece that combines their powers should be worth less than the value of Knight+Queen, not more.

I agree that 10x10 board size will tend to increase the value of unlimited range pieces.  On the other hand, the SAC chess board is rather crowded, and this may tend to decrease the value of ranged pieces (while increasing the relative value of the knight's unblockable movement). SAC chess starts with 60% of the board occupied, as opposed to 50% for FIDE chess.

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