Stopping times in the game Rock-Paper-Scissors

TL;DR

This paper analyzes the stopping times in Rock-Paper-Scissors using recurrence relations and Markov chains, revealing that mean stopping times grow exponentially with the number of players.

Contribution

It introduces a novel approach combining recurrence relations and Markov chain analysis to compute and understand stopping times in the game.

Findings

Mean stopping times increase exponentially with players

Distribution of stopping times derived from Markov chain analysis

Recurrence relations effectively compute mean stopping times

Abstract

In this paper we compute the stopping times in the game Rock-Paper-Scissors. By exploiting the recurrence relation we compute the mean values of stopping times. On the other hand, by constructing a transition matrix for a Markov chain associated with the game, we get also the distribution of the stopping times and thereby we compute the mean stopping times again. Then we show that the mean stopping times increase exponentially fast as the number of the participants increases.