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1 results

  • On the waiting time in a janken game

  • Part of
  • Hiroshi Maehara, Sumie Ueda
  • Journal:
    Journal of Applied Probability / Volume 37 / Issue 2 / June 2000
    Published online by Cambridge University Press:
    14 July 2016, pp. 601-605
    Print publication:
    June 2000

  • 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 Wn be the number of rounds played through the game. Among other things, it is proved that (2/3)nWn 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.