An Analysis of Probability Thought in Ancient Chinese Dice Game Culture

The manual Chuhong pu (除红谱, Red Fours Out) describes a seminal ancient Chinese dice game. Compiled by Yang Weizhen (杨维祯), a scholar active during the Yuan and early Ming dynasties, and based on Zhu He (朱河)'s original Song-dynasty work, the book sets out the rules for the simultaneous rolling of four dice, with outcomes determined by the combinations of points rolled. The game of Chuhong boasts a long history and diverse applications, and was frequently played at banquets, card games, and casinos. Pre-modern literati particularly favored the game when paired with elegant drinking games. This paper traces the transmission lineage of the manual and explores its cultural significance. It analyzes and verifies the game's rules and fairness through probabilistic calculations using a simplified model. The analysis demonstrates that the manual adheres to fairness in its design. By comparing rule adjustments across different editions, the paper also reveals that individuals during the Ming and Qing dynasties had already developed a comprehensive understanding of the frequency distribution of various point combinations through extensive practice. This allowed them to refine the rules based on this understanding, demonstrating a rudimentary grasp of probabilistic thinking.