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Quantitative Rule-Based Strategy modeling in Classic Indian Rummy: A Metric Optimization Approach

Purushottam Saha, Avirup Chakraborty, Sourish Sarkar, Subhamoy Maitra, Diganta Mukherjee, Tridib Mukherjee

TL;DR

The paper addresses strategic play in the 13-card Classic Indian Rummy under imperfect information by introducing MinDist, a distance-based hand metric that complements the traditional MinScore. It develops a tractable rule-based framework using dynamic programming and bitmask representations, augmented by a Super Joker concept to handle unobserved cards, and augments strategies with simple opponent modeling. Empirical evaluation in a two-player zero-sum setting demonstrates that MinDist-based agents—especially when combined with opponent modeling—achieve statistically significant gains over MinScore-based and random baselines, with a clear skill gradient. The work provides an interpretable, formal baseline for algorithmic Rummy strategy design and highlights avenues for dynamic, belief-aware extensions and learning-based integration.

Abstract

The 13-card variant of Classic Indian Rummy is a sequential game of incomplete information that requires probabilistic reasoning and combinatorial decision-making. This paper proposes a rule-based framework for strategic play, driven by a new hand-evaluation metric termed MinDist. The metric modifies the MinScore metric by quantifying the edit distance between a hand and the nearest valid configuration, thereby capturing structural proximity to completion. We design a computationally efficient algorithm derived from the MinScore algorithm, leveraging dynamic pruning and pattern caching to exactly calculate this metric during play. Opponent hand-modeling is also incorporated within a two-player zero-sum simulation framework, and the resulting strategies are evaluated using statistical hypothesis testing. Empirical results show significant improvement in win rates for MinDist-based agents over traditional heuristics, providing a formal and interpretable step toward algorithmic Rummy strategy design.

Quantitative Rule-Based Strategy modeling in Classic Indian Rummy: A Metric Optimization Approach

TL;DR

The paper addresses strategic play in the 13-card Classic Indian Rummy under imperfect information by introducing MinDist, a distance-based hand metric that complements the traditional MinScore. It develops a tractable rule-based framework using dynamic programming and bitmask representations, augmented by a Super Joker concept to handle unobserved cards, and augments strategies with simple opponent modeling. Empirical evaluation in a two-player zero-sum setting demonstrates that MinDist-based agents—especially when combined with opponent modeling—achieve statistically significant gains over MinScore-based and random baselines, with a clear skill gradient. The work provides an interpretable, formal baseline for algorithmic Rummy strategy design and highlights avenues for dynamic, belief-aware extensions and learning-based integration.

Abstract

The 13-card variant of Classic Indian Rummy is a sequential game of incomplete information that requires probabilistic reasoning and combinatorial decision-making. This paper proposes a rule-based framework for strategic play, driven by a new hand-evaluation metric termed MinDist. The metric modifies the MinScore metric by quantifying the edit distance between a hand and the nearest valid configuration, thereby capturing structural proximity to completion. We design a computationally efficient algorithm derived from the MinScore algorithm, leveraging dynamic pruning and pattern caching to exactly calculate this metric during play. Opponent hand-modeling is also incorporated within a two-player zero-sum simulation framework, and the resulting strategies are evaluated using statistical hypothesis testing. Empirical results show significant improvement in win rates for MinDist-based agents over traditional heuristics, providing a formal and interpretable step toward algorithmic Rummy strategy design.
Paper Structure (12 sections, 4 equations, 6 figures, 2 tables, 2 algorithms)

This paper contains 12 sections, 4 equations, 6 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Game Rules
  3. Related Work
  4. Metric Formulation
  5. MinScore
  6. Proposed MinDist Metric
  7. Algorithmic Framework
  8. On Correctness of the MinDist Algorithm
  9. Opponent Hand modeling
  10. Simulation Framework
  11. Results
  12. Discussion and Conclusion

Figures (6)

  • Figure 1: MinScore eCDF (clipped at 80)
  • Figure 2: MinScore histogram (unclipped)
  • Figure 3: MinDist histogram
  • Figure 4: Example MinScore DP transitions for a given hand
  • Figure 5: Pairwise Win Rate between strategies
  • ...and 1 more figures