Every beginner that has pickup a chess book has seen a table listing the value of each piece. A quick recap of this table: Queen-9 Rook-5 Bishop-3.5 Knight-3 Pawn-1. Okay, some might have spot that I use the non-traditional aproach of not assigning the bishop and knight the same value. The agrument for using this table is that bishops are usally more preferable to have because most positions are likely to become open at some point in time. 

Well, I'm not interested in stating correct values for the pieces because the truth is the values change from position to position, the only value that remains constant is the King. How do we know the values change? Because were willing to give up are queen if we can force mate. An logical agrument of this: I sac the queen to open lines to the king. (Maybe one or two pawns are gain so givenup 9 points for 2 so far) But I have a Rook and bishop in perfect position now to take advantage of the exposed king. How do we assign values now? Has the queen lost in value or have the bishop and rook gain in value. I think a little of both has happen but the main point is that something has occur to change their values and that was the weakness of the enemy's King.

In Rethinking the Chess Pieces by Andrew Soltis list the criteria of what exactly contributes to a piece arbituary value.  Its mobility, targets, range, cooperation or redundancy, and its "personality". Lets define each of these terms for better understanding of what exactly makes a piece worthwile.  Mobility - the greater of possible moves a piece has the more valuable it can become.  Targets - a area of weakness which pressure can be apply to. A piece become less valuable if it can't target a weakness. Range - area of which the piece is constrain to. If we play with a 10x10 board the queens and rooks would become even stronger and if the board was reduced to 5x5 the knights would increase in value while the queen would actually prove less effective. Cooperation or Redudancy - are the pieces communicating well with each other in the position.  An example would be having a knight blocking a bishops diagonal in some positions the bishop is supplying support while in others the knight is in the way of the bishop's scope. Personality - is a term use for describing different piece match ups. For example a rook does very well when facing pawns but its more difficult for a knight. 

The importance of the non-static nature of piece values is that it becomes harder to evaluate when a knight is equal to 3 pawns or when two minors equals a rook and a pawn.

I look forward to insvestigate this in more detail and hopefully I will be able to show these ideas with practical examples with the motivation of how this information can be applied.