Single Comment

Muller, thank you for your analysis.  You gave me some things to think about.  However, I'm still not sure we're entirely on the same page.

You mention the Wazir, and how it's barely worth more than a pawn.  So I asked myself, why would that be?  I now hear that the analogous-but-diagonal Ferz is considered more valuable, despite being colorbound.  Why would that be?  They have equal "firepower".  A little thought produces the answer.  The Wazir is devalued by its lack of mobility, especially on a board crowded with pawns (and others).   A Ferz can easily slip through pawn formations (which depend on diagonals), but a Wazir cannot.

These same considerations will impact a Rook when compared to a Bishop.  With that in mind, it seems likely that the colorbound nature of the Bishop does affect its value, but this probably does little more than balance the pawn-bound limitations of the Rook.

This also explains the phenomena you discuss.  A rook/knight combo breaks the rook's pawn-bound status, and is probably more valuable than a knight+rook as separate pieces.  A bishop/knight combo breaks the bishops color-bound status, and is probably more valuable than a knight+bishop as separate pieces.

But a queen already breaks both these limitations, and a Knight's powers probably don't break them much further than they are already broken.  I therefore still doubt very much that an Amazon is worth more than the combined value of Queen + Knight.  

The pawn-synergy factor brings me back to my original point.  The value of a piece will depend on what else is on the board and the synergy or lack thereof between them.  "Sac Chess" throws us all for a loop by radically altering the other pieces on the board.  It's guesswork, and the value of a piece as measured in one context (such as a close approximation of FIDE Chess), will not necessarily apply here.