Pawn: 2 pts
Bishop: 2.5 pts
Rook: 3 pts
Knight: 3.5 pts
Queen: 5.5 pts
King: Infinite pts(You lose the king, you lose the game.)
Pawn: 2 pts
Bishop: 2.5 pts
Rook: 3 pts
Knight: 3.5 pts
Queen: 5.5 pts
King: Infinite pts(You lose the king, you lose the game.)
From a mathematical standpoint...
The king is worth 0 points for this challenge for the sake of simplification. Infinity would be pointless. Infinity cannot be substracted from Infinity, as they are not part of the set of a number system: the result of the substraction would be undefined. Infinity is not a number, it is a concept.
As there must be exactly two kings on the board, one of each color, the sum of their values (if they are part of the complex number system) always equals 0 anyway (but not if you use Infinity, one of the few problematic values you could've presented). The white king could be worth 0, 41, 45i, 712, 20231216 points, and the black king its value multiplied by -1, it wouldn't matter here.
Computers «cheat»/deal with this by having a special value assigned to the concepts of Infinity (and -Infinity).
I am open to suggestions
. You are welcome to present your own «piece value optimisation crafting challenges» here.