What's the Best Seat in the Game Left, Center, Right?

TL;DR

This paper analyzes the dice game Left, Center, Right using Markov chain and Monte Carlo methods to compute game length and winning probabilities, revealing surprising results and proposing a fairness-enhancing rule change.

Contribution

It introduces a detailed probabilistic analysis of the game and suggests a simple rule modification to improve fairness among players.

Findings

Expected game length varies with number of players.

Winning probabilities differ significantly among players.

A small rule change can make the game more equitable.

Abstract

Left, Center, Right is a popular dice game. We analyze the game using Markov chain and Monte Carlo methods. We compute the expected game length for two to eight players and determine the probability of winning for each player in the game. We discuss the surprising conclusions of which players have the highest and lowest chance of winning, and we propose a small rule change that makes the game a little more fair.