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

TL;DR

Left, Center, Right is a popular dice game analyzed using Markov chain and Monte Carlo methods and the surprising conclusions of which players have the highest and lowest chance of winning are discussed.

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.

Figures (5)

• Figure 1: When the players 1 through 3 have two, three, and one chips, respectively, and it is player 1's turn, there are ten possible outcomes.
• Figure 2: These are the transition probabilities when the players 1 through 3 have two, three, and one chips, respectively, and it is player 1's turn.
• Figure 3: Probability of victory for games of two to eight players (with error bars for those computed using Monte Carlo methods).
• Figure 4: The probability of victory for 50 players.
• Figure 5: Probability of victory in an eight-player game under the ordinary (red circles) and modified (blue squares) rule.