Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2019; 56(6): 1497-1510

Online first article June 10, 2019      Printed November 30, 2019

https://doi.org/10.4134/BKMS.b181218

Copyright © The Korean Mathematical Society.

Stopping times in the game Rock-Paper-Scissors

Kyeonghoon Jeong, Hyun Jae Yoo

Seoul National University; Hankyong National University

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.

Keywords: the game Rock-Paper-Scissors, Markov chain, stopping times

MSC numbers: 60G40, 60J20

Supported by: The research by H. J. Yoo was supported by Basic Science Research Program through the National Research
Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016 R1D1A1B03936006)