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Ha, then I sure fooled a lot of people. Always said I couldn't play the game. ;-)

Regardless of my skills, HG, do you contend that the value of a specific chess piece is in some sense invariant? Well, invariant across the range of reasonable chess games, anyhow, on effectively standard 2D boards. Clearly, a non-standard board can drastically change piece values. Consider a rectangular lattice, a diagonal lattice, a Byzantine board, and a 3D board. The exact shape of the edges also makes a difference, most notably in mating. The file count can be even or odd, making a difference in types or [initial] placement of pieces, and the values of bound pieces are affected by rank and file counts. But that's not what we're looking at. Flat, 2D, essentially rectilinear boards [without too many holes in them] are the playing surface in 90+% of games, so we'll stick to that. And ignore the 'parity' of the board, always assuming the board is perfectly fair. It's a legitimate simplifying assumption.

Having disposed of terrain, we look at environment. There are 2 ways to look at environment. The first is the most common. To illustrate, the rook is of zero practical value in the beginning of the FIDE game, and it grows in power/usability as the game goes on. Betza makes a similar comment about the commoner. It seems to me both statements are obviously true. One could even say they are trivially true. In the past, HG, you have successfully argued this observation is essentially trivial, the rook is 5 in value and the knight is 3, even though there are tactical situations where a knight is worth more than a rook. Does that hold true for all environments, though? To be continued later.