Automatic Design of Balanced Board Games

AI techniques are already widely used in game software to provide computer-controlled opponents for human players. However, game design is a more-challenging problem than game play. Designers typically expend great effort to ensure that their games are balanced and challenging. Dynamic game-balancing techniques have been developed to modify a game-engine’s parameters in response to user play. In this paper we describe a first attempt at using AI techniques to design balanced board games like checkers and Go by modifying the rules of the game, not just the rule parameters. Our approach involves the use of a commercial general game-playing (GGP) engine that plays according to rules that are specified in a general game-definition language. We use a genetic algorithm (GA) to search the space of game rules, looking for turn-based board games that are well balanced, i.e., those that the GGP engine in self-play finds equally hard to win from either side and rarely draws. The GA finds better games than a randomsearch strategy that uses equivalent computational effort. Introduction & Overview The earliest examples of computer-controlled game play were AI programs that were specific to a particular game like chess. More recently, General Game Playing (CGP) has emerged as its own area of research: CGP software is capable of playing any game whose rules are specified in a given scripting language (Pell 1992, Reference B, Genesereth 2005). Much research has gone into making both specific and general game-playing software as capable as possible. However, there is more to making a game interesting than just providing a capable opponent. The qualities of the game itself are important. In particular, most good games are balanced in the sense that they provide just enough challenge to make play enjoyable, but not so much that play is frustrating (Adams 2007). The notion of using AI techniques to dynamically change game-play parameters to achieve dynamic game balancing (DGB) has recently been investigated by several research teams (Demasi 2002, Hunicke 2004, Spronck 2004, Andrade 2005). Copyright © 2007, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Another way to automatically achieve balance in computer games is to not just adjust the game parameters, but to change the actual rules of the game. We call this Automatic Game Design (AGD). AGD has not yet been studied systematically. In 2004 it was reported in the press that Jim Lewis, an inventor from New Jersey, had used a computer to develop an especially difficult form of the well-known sliding-block puzzle (Reference A). Lewis computed the trees of all possible moves from the initial configurations of multiple candidate puzzles. The puzzle that produced the broadest and tallest tree he dubbed Quzzle, which can now be bought at various sites on the Internet. However, Lewis’s general approach of comparing games by considering the shape and size of the corresponding move trees is not a practical approach for AGD, nor is it backed by any theory equating game quality purely to the size of its search space. Puzzle aficionados consider Quzzle to be less interesting than many other sliding-block puzzles that were designed by hand (Pegg 2004). In contrast, our approach to AGD is to generate wellbalanced board games that are won evenly by both the first-moving and second-moving players and that result infrequently in a draw. Our work is based on a commercially available GGP called Zillions of Games (ZOG). ZOG is a universal gaming engine that allows the creation of many kinds of board games (Reference C). Games rules are specified in a custom scripting language. A collection of scripting commands is called a Zillions Rules File (ZRF). There are three major components of a ZRF: the board, the pieces, and the victory condition. The board definition specifies the players, turn order, the board dimensions, the number of pieces that each player has at the beginning of the game, and the initial placement of pieces on the board. The piece definition characterizes the allowable behavior of game pieces. Here each piece’s movement options are enumerated. Last, the victory condition defines the possible outcomes of the game. Here is an example of a ZRF for a simple game, Tic-Tac-Toe: