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Skill vs. Chance Quantification for Popular Card & Board Games

Tathagata Banerjee, Anushka De, Subhamoy Maitra, Diganta Mukherjee

TL;DR

This work develops a data-driven framework to quantify the role of skill versus chance in four popular games by modeling win-rate dynamics as a function of experience, using transformed win rates and empirical bootstrap to assess uncertainty. It demonstrates a robust, multi-source confirmation of skill being a strong component in Chess, with Rummy and Ludo showing meaningful but more variable skill contributions, and Teen Patti displaying comparatively weaker skill signals. A flexible final Skill Score combines learning and innate skill into a comparative ranking, highlighting how different game mechanics influence learnability and strategic depth. The framework is transparent, adaptable to other formats and metrics, and has potential applications in legal classification, game design, and player-performance analysis.

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.

Skill vs. Chance Quantification for Popular Card & Board Games

TL;DR

This work develops a data-driven framework to quantify the role of skill versus chance in four popular games by modeling win-rate dynamics as a function of experience, using transformed win rates and empirical bootstrap to assess uncertainty. It demonstrates a robust, multi-source confirmation of skill being a strong component in Chess, with Rummy and Ludo showing meaningful but more variable skill contributions, and Teen Patti displaying comparatively weaker skill signals. A flexible final Skill Score combines learning and innate skill into a comparative ranking, highlighting how different game mechanics influence learnability and strategic depth. The framework is transparent, adaptable to other formats and metrics, and has potential applications in legal classification, game design, and player-performance analysis.

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.

Paper Structure

This paper contains 28 sections, 11 equations, 9 figures, 21 tables.

Table of Contents

  1. Introduction
  2. The Game Structures Considered
  3. Algorithmic Approach
  4. Framework for Empirical Analysis
  5. Data Format
  6. Our Luck vs. Law measurement formulation
  7. Estimation Strategy
  8. Assessing Robustness using Resampling
  9. Analyzing Chess
  10. Classical
  11. Rapid, one year data
  12. Rapid, two year data
  13. Online Chess Data
  14. Regression Results
  15. Bootstrap Results
  16. ...and 13 more sections

Figures (9)

  • Figure 1: Histogram of Bootstrap Estimates of Regression Coefficients
  • Figure 2: Bootstrapping Results for 2-Player Rummy Regression Model
  • Figure 3: Histogram of Bootstrap Estimates of Regression Coefficients
  • Figure 4: Histogram of Bootstrap Estimates of Regression Coefficients (Teen Patti-No Limit)
  • Figure 5: Histogram of Bootstrap Estimates of Regression Coefficients (Teen Patti-Regular)
  • ...and 4 more figures