Freestyle Player-Balancing: A Novel Flexible Framework for Addressing Game Balance and Opening Memorization in Decisive, Two-Player, Perfect-Information, Turn-Based Games

Decisive, two-player, perfect-information, turn-based games are central to game theory. However, achieving game balance in these games is challenging, and opening memorization is boring and exhausting for human players. In this paper, we propose a novel flexible framework Freestyle Player-Balancing to address the two problems. The framework preserves core dynamics of the original games. It consists of three phases: the Safe Move Phase, the Decision Phase and the Fight Phase. In the Fight Phase, the games start with fight-starting positions and the rules are the same as original games’. The fight-starting positions are determined in the Decision Phase, and players can decide when and how to get into the Decision Phase from the Safe Move Phase. They can also choose to make optimal safe moves to stay in the Safe Move Phase. Game balance solvability depends on game complexity. We proved that if a game is not strongly solved, the game balance problem can be alleviated by the framework for human players. We also demonstrated Freestyle Player-Balancing shares similarities with bidding. The framework can also mitigate the opening memorization problem by setting a minimal length of the Safe Move Phase. Draw problem is serious in many win-loss-draw games and can be transformed into the game balance problem, and then tackled by the framework. With the Framework, we conducted a few case studies in chess, xiangqi, Go, Hex, etc. The results show the Freestyle Player-Balancing can mitigate the game balance problem and opening memorization problem.