How to Generalize Janken – Rock-Paper-Scissors-King-Flea

  • Hiro Ito
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8296)


Janken, which is a very simple game and it is usually used as a coin-toss in Japan, originated in China, and many variants are seen throughout the world. A variant of janken can be represented by a tournament, where a vertex corresponds a sign and an arc (x,y) means sign x defeats sign y. However, not all tournaments define useful janken variants, i.e., some janken variants may include a useless sign, which is strictly inferior than another sign in any case. We first shows that for any positive integer n except 2 and 4, we can construct a janken variant with n signs without useless signs. Next we introduces a measure of amusement of janken variants by using the variation of the difference of out-degree and in-degree. Under this measure, we show that a janken variant has the best amusement among ones with n signs if and only if it corresponds to one of the tournaments defined by J. W. Moon in 1993. Following these results, we present a janken variant “King-fles-janken,” which is the best amusing janken variant among ones with five signs.


Positive Integer Simple Game Open Hand Australasian Journal Extra Sign 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hiro Ito
    • 1
  1. 1.School of Informatics and EngineeringThe University of Electro-CommunicationsChofuJapan

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