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While I'd say your points are mostly... on... point, I'd disagree that pieces have different value in a concrete way.

Any piece's value at any given time is directly related to how much it contributes to protecting your king, attacking the opponent's king, or both. At the start, your pawns are worthless by this measure; however, further on in the game, they can be instrumental in limiting an opponent's movements and avoiding potential check situations. But that value, and all other pieces' value, are constantly in flux -- and your opponent's attempt to figure out which are the most valuable pieces to you is the process of trying to read a player's next few moves.

Which I think speaks to Greg Karber's opinion above: The king's importance creates the central goal and drama of the game.

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Oh, I quite like that! *furiously jots it down*

I'll admit I was approaching it from a more arbitrary 'points = vale' angle. Looking at my notes again, I see why I was doing that (to simplify some of  the complexity in interactions). 

While I agree that a piece's value in context is wildy variable, I also think from a purely utilitatrian perspective (subtracting any other factors) that a bishop  or rook, for instance, are more 'useful' than a pawn--one of  the minor objectives, after all, is the push to upgrade one's pawn if possible.

Which I think speaks to Greg Karber's opinion above: The king's importance creates the central goal and drama of the game

You know, that's an interesting point. I was aware of this but hadnt given it much thought! Makes me wonder if swapping out the King for another piece (pawns  or rooks) would mix things up in a good way or not. Perhaps considering the game lost if all of those units are captured. 

Might make for an interesting puzzle scenario, hmm.