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

TL;DR

This paper analyzes two variants of Ludo with multiple dice, comparing strategic play through simulations, game theory, and Nash Equilibrium, revealing how strategy effectiveness varies with game length and complexity.

Contribution

It introduces a comprehensive analysis of strategic dominance in two Ludo variants, including the computation of Nash Equilibria and their dependence on game length.

Findings

More sophisticated strategies outperform naive ones.

Optimal strategies shift with game length.

Some strategies counter each other in competitive play.

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.