Skill vs. Chance Quantification for Popular Card & Board Games

Abstract: This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from four popular games Chess, Rummy, Ludo, and Teen Patti, using empirical win statistics across varying levels of experience. By modeling win rate as a function of experience through a regression framework and employing empirical bootstrap resampling, we estimate the degree to which outcomes improve with repeated play. To summarize these dynamics, we propose a flexible skill score that emphasizes learning over initial performance, aligning with practical and regulatory interpretations of skill. Our results reveal a clear ranking, with Chess showing the highest skill component and Teen Patti the lowest, while Rummy and Ludo fall in between. The proposed framework is transparent, reproducible, and adaptable to other game formats and outcome metrics, offering potential applications in legal classification, game design, and player performance analysis.