1. Introduction

Nothing is more difficult than the art of maneuvering for advantageous positions.
    Sun-Tzu (~400 BC)

In the big picture, whether the [chess] computer beats us isn't important. Either way, it's a human triumph. In fact, it's a greater human triumph when the computer wins. As a player, you can conceive a brilliant move without understanding where it came from. As a programmer, you have to do something much harder: articulate rules that will generate such brilliance. - "We've Made Our Match", William Saletan, Sunday, May 13, 2007; Page B02 Washington Post

The challenge: How might we create an evaluation function for a computer chess program that plays a stronger positional game of chess? Solutions should ideally have utility for both real-time game playing and for analysis of completed games.

This article is concerned with the problem of constructing a computing routine or "program" for a modern general purpose computer which will enable it to play chess.

Specifically, this article is concerned with heuristic algorithms. A heuristic is anything that provides a plausible aid or direction in the solution of a problem but is in the final analysis unjustified, incapable of justification, and potentially fallible [from Koen, Discussion of the Method, p.28]. Heuristics help solve unsolvable problems or reduce the time needed to find a satisfactory solution.

From wikipedia: Aron Katsenelinboigen has discussed the positional style of playing a chess game.

The positional style is distinguished by

1. a positional goal and
2. a formation of semi-complete linkages between the initial step and final outcome. Katsenelinboigen declares

“Unlike the combinational player, the positional player is occupied, first and foremost, with the elaboration of the position that will allow him to develop in the unknown future. In playing the positional style, the player must evaluate relational and material parameters as independent variables. ( … ) The positional style gives the player the opportunity to develop a position until it becomes pregnant with a combination. However, the combination is not the final goal of the positional player—it helps him to achieve the desirable, keeping in mind a predisposition for the future development. The Pyrrhic victory is the best example of one’s inability to think positionally.”[8]

The positional style serves to

a) create a predisposition to the future development of the position;
b) induce the environment in a certain way;
c) absorb an unexpected outcome in one’s favor;
d) avoid the negative aspects of unexpected outcomes.

The positional style gives the player the opportunity to develop a position until it becomes pregnant with a combination. Katsenelinboigen writes:
“As the game progressed and defense became more sophisticated the combinational style of play declined. . . . The positional style of chess does not eliminate the combinational one with its attempt to see the entire program of action in advance. The positional style merely prepares the transformation to a combination when the latter becomes feasible.”[9]

[8] V. Ulea, The Concept of Dramatic Genre and The Comedy of A New Type. Chess, Literature, and Film. Southern Illinois University Press, 2002, p.p.17-18])
[9] Selected Topics in Indeterministic Systems Intersystems Publications: California, 1989, p. 21

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