A Metric for Entertainment of Boardgames: Its Implication for Evolution of Chess Variants

This research introduces a quantitative metric to evaluate the entertainment value of board games, specifically focusing on the evolutionary trajectory of chess variants. The proposed entertainment measure, E(G), is derived from the relationship between the average number of plausible moves and the average game length. The study posits that as E(G) decreases, the entertainment impact of a game increases, suggesting that the historical evolution of chess-like games represents an optimization process where rules were refined to balance strategic complexity with player engagement.

To test this hypothesis, the study analyzes both modern games—using grandmaster data—and ancient variants, such as Chaturanga, Shatranj, and various medieval iterations, using computer self-play simulations. These simulations utilized material-based evaluation functions and look-ahead depths of three to five plies to generate statistical data on move counts, game duration, and draw rates. The findings reveal that chess variants have historically evolved along two distinct paths: one characterized by increasing search-space complexity and another by the refinement of rules to lower E(G) and reduce draw rates.

The analysis concludes that modern chess represents a highly matured state of this evolutionary process, achieving a stable equilibrium between search-space complexity and entertainment impact. By incorporating powerful pieces like the Queen and modern promotion rules, the game effectively reduced excessive game lengths and draw frequencies found in earlier, more cumbersome variants. The study suggests that this framework for measuring entertainment and complexity is applicable to other board games, such as Shogi and Xiangqi, providing a robust method for understanding the natural selection of game rules throughout history.