On the waiting time in a janken game

Consider a janken game (scissors-paper-rock game) started by n players such that (1) the first round is played by n players, (2) the losers of each round (if any) retire from the rest of the game, and (3) the game ends when only one player (winner) is left. Let W n be the number of rounds played thr...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied probability 2000-06, Vol.37 (2), p.601-605
Main Authors: Maehara, Hiroshi, Ueda, Sumie
Format: Article
Language:English
Subjects:
60E99
60F99
Applied sciences
asymptotic distribution
Distribution theory
Exact sciences and technology
Game theory
Janken
Limit theorems
Mathematics
Operational research and scientific management
Operational research. Management science
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
scissors-paper-rock
Short Communications
waiting time
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Consider a janken game (scissors-paper-rock game) started by n players such that (1) the first round is played by n players, (2) the losers of each round (if any) retire from the rest of the game, and (3) the game ends when only one player (winner) is left. Let W n be the number of rounds played through the game. Among other things, it is proved that (2/3) n W n is asymptotically (as n → ∞) distributed according to the exponential distribution with mean ⅓, provided that each player chooses one of the three strategies (scissors, paper, rock) with equal probability and independently from other players in any round.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1014842562