New Ideas in Calculating Values

Rock, Paper, Scissors

Part of the value of a piece depends on how that piece interacts with the other pieces on the board.

There may be two pieces such that they are of equal value, but one always beats the other. Rock breaks scissors, scissors cut paper, paper covers rock....

Distance

How far a jumper jumps, or how far a runner runs, is important for more than one reason. In the context of this chapter, it is important because an advantage in reach distance often gives one piece the advantages of stealth and/or domination.

In the game pitting Bishops versus FADs, you might notice that the Bishops, despite being weaker than the FADs, were able to do quite well for a long time by taking advantage of their long-distance powers.

Domination

In the language of endgame studies, a Bishop on c5 is said to "dominate" a Knight on c8: the Knight is not attacked, but the squares to which it can move are all attacked by the Bishop (and the Knight, if not actually trapped, can be traded off at will).

Conversely, with a Pawn blocking c4 a Knight on f4 dominates a Bishop on f1; Bishops and Knights can dominate each other.

A Rook can dominate a Knight, but cannot dominate a Bishop; because of this, the Pawnless endgame of Rook-versus-Knight is much easier to win than Rook-versus-Bishop.

Can-Mate

The King is always on the board, so the way that a piece interacts with Kings is bound to be important.

The WD is about as strong as the Knight, but the Pawnless endgame of K+WD versus K is a win. Therefore, the endgame K+WD+P versus K+N is almost always a win.

This gives the WD a certain advantage in the endgame, which helps make up for its other weaknesses.

Pawn Cooperation

Pawns are also always in the game, so the way a piece works with pawns is important.

However, there are many ways to relate to Pawns.

Bishops and Pawns defend each other nicely, but then have trouble advancing; a Knight can defend a Pawn, or help its advance, but not both at once (and yet Knights and Pawns do work well together in general); Rooks can get behind and push, but then cannot attack the advance-square, or they can get in front and pull, but then they get in the way at the end. The clumsy WD can run a Pawn down to the goal line, but is a bit slow; the WA is not a good shepherd.

Stealth

When piece A can attack piece B without in turn being attacked by piece B, then piece A is stealthy with respect to piece B.

In FIDE-chess, Knights are mutually stealthy with everything else.

I have found stealth to be less important than I had expected.

Summary

Distance, dominations, and can-mate are the important factors.

I wonder if you could design two armies such that one would be noticeably stronger than FIDE-chess, the other weaker, but when they fought each other the weaker would have an advantage...

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