An Evaluation Function for the Game of Amazons

This analysis details the development and implementation of an evaluation function for the computer program AMAZONG, designed to play the game of Amazons. The primary thesis is that a sophisticated, multi-phase evaluation function—specifically one that accounts for both territorial control and the mobility of individual pieces—is essential for competitive play. By integrating these metrics, the program can effectively navigate the transition from the opening phase through the main game and into the final filling phase.

The evaluation function relies on two primary distance metrics: the minimal number of chess Queen moves and the minimal number of chess King moves required to reach a square. These metrics allow the program to estimate territorial access and identify potential zugzwang situations. A critical innovation is the inclusion of a mobility correction term, which identifies and punishes enclosed or passive amazons. This feature enables the program to proactively trap opponent pieces, a strategy that proved decisive during the 2002 Computer Olympiad in Maastricht, where AMAZONG secured a tournament victory.

The methodology involves a weighted combination of territorial and positional parameters that shift in importance as the game progresses. The program calculates the expected number of moves until the filling phase to dynamically adjust these weights, ensuring the evaluation remains relevant throughout the game. While the program currently utilizes a machine-generated opening book of over 30,000 moves, the evaluation function remains the core driver of its performance. Future refinements are proposed to better handle large territorial frameworks and the complex interactions between multiple amazons in confined regions, addressing the current limitations in long-term strategic planning.