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Skill Dominance Analysis of Two(Four) player, Three(Five) dice Variant of the Ludo Game

Tathagata Banerjee, Diganta Mukherjee

TL;DR

A clear distinction between performances of strategies is observed, with more sophisticated strategies beating the naive one, and a gradual shift in optimal strategy profiles is observed with changing game length.

Abstract

This paper examines two different variants of the Ludo game, involving multiple dice and a fixed number of total turns. Within each variant, multiple game lengths (total no. of turns) are considered. To compare the two variants, a set of intuitive, rule-based strategies is designed, representing different broad methods of strategic play. Game play is simulated between bots (automated software applications executing repetitive tasks over a network) following these strategies. The expected results are computed using certain game theoretic and probabilistic explanations, helping to understand the performance of the different strategies. The different strategies are further analyzed using win percentage in a large number of simulations, and Nash Equilibrium strategies are computed for both variants for a varying number of total turns. The Nash Equilibrium strategies across different game lengths are compared. A clear distinction between performances of strategies is observed, with more sophisticated strategies beating the naive one. A gradual shift in optimal strategy profiles is observed with changing game length, and certain sophisticated strategies even confound each other's performance while playing against each other.

Skill Dominance Analysis of Two(Four) player, Three(Five) dice Variant of the Ludo Game

TL;DR

A clear distinction between performances of strategies is observed, with more sophisticated strategies beating the naive one, and a gradual shift in optimal strategy profiles is observed with changing game length.

Abstract

This paper examines two different variants of the Ludo game, involving multiple dice and a fixed number of total turns. Within each variant, multiple game lengths (total no. of turns) are considered. To compare the two variants, a set of intuitive, rule-based strategies is designed, representing different broad methods of strategic play. Game play is simulated between bots (automated software applications executing repetitive tasks over a network) following these strategies. The expected results are computed using certain game theoretic and probabilistic explanations, helping to understand the performance of the different strategies. The different strategies are further analyzed using win percentage in a large number of simulations, and Nash Equilibrium strategies are computed for both variants for a varying number of total turns. The Nash Equilibrium strategies across different game lengths are compared. A clear distinction between performances of strategies is observed, with more sophisticated strategies beating the naive one. A gradual shift in optimal strategy profiles is observed with changing game length, and certain sophisticated strategies even confound each other's performance while playing against each other.
Paper Structure (16 sections, 9 figures, 7 tables)

This paper contains 16 sections, 9 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Game Description: Generic Ludo
  3. First New Variant of the Game: 2-player, 3-dice version
  4. Second New Variant of the Game: 4-player, 5-dice version
  5. Nash Equilibrium on Expected Path
  6. 2-player, 3-dice version
  7. 4-player, 5-dice version
  8. Specification of Players' Intuitive Rule-based Strategies for Empirical Evaluation
  9. The "Naive" Player (N)
  10. The "Aggressive" Player (A)
  11. The "Responsible Pair" Player (RP)
  12. Empirical Results
  13. 2-player, 3-dice version
  14. 4-player, 5-dice version
  15. Empirical Nash Equilibrium
  16. ...and 1 more sections

Figures (9)

  • Figure 1: Win Proportion of strategy combinations 1-27 in 16-turn game
  • Figure 2: Win Proportion of first strategy combinations 28-54 in 16-turn game
  • Figure 3: Win Proportion of strategy combinations 55-81 in 16-turn game
  • Figure 4: Win Proportion of strategy combinations 1-27 in 12-turn game
  • Figure 5: Win Proportion of first strategy combinations 28-54 in 12-turn game
  • ...and 4 more figures

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • Remark 3