Hanabi is NP-complete, even for cheaters who look at their cards

Jean Francois Baffier, Man Kwun Chiu, Santiago Diez Donoso, Cozzetti Matias Korman, Valia Mitsou, André Van Renssen, Marcel Roeloffzen, Yushi Uno

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

This paper studies a cooperative card game called Hanabi from an algorithmic combinatorial game theory viewpoint. The aim of the game is to play cards from 1 to n in increasing order (this has to be done independently in c different colors). Cards are drawn from a deck one by one. Drawn cards are either immediately played, discarded or stored for future use (overall each player can store up to h cards). The main feature of the game is that players know the cards their partners hold (but not theirs. This information must be shared through hints). We introduce a simplified mathematical model of a single-player version of the game, and show several complexity results: the game is intractable in a general setting even if we forego with the hidden information aspect of the game. On the positive side, the game can be solved in linear time for some interesting restricted cases (i.e., for small values of h and c).

Original languageEnglish
Title of host publication8th International Conference on Fun with Algorithms, FUN 2016
EditorsErik D. Demaine, Fabrizio Grandoni
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770057
DOIs
Publication statusPublished - 2016 Jun 1
Event8th International Conference on Fun with Algorithms, FUN 2016 - La Maddalena, Italy
Duration: 2016 Jun 82016 Jun 10

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume49
ISSN (Print)1868-8969

Other

Other8th International Conference on Fun with Algorithms, FUN 2016
CountryItaly
CityLa Maddalena
Period16/6/816/6/10

Keywords

  • Algorithmic combinatorial game theory
  • Sorting

ASJC Scopus subject areas

  • Software

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  • Cite this

    Baffier, J. F., Chiu, M. K., Diez Donoso, S., Korman, C. M., Mitsou, V., Van Renssen, A., Roeloffzen, M., & Uno, Y. (2016). Hanabi is NP-complete, even for cheaters who look at their cards. In E. D. Demaine, & F. Grandoni (Eds.), 8th International Conference on Fun with Algorithms, FUN 2016 [4] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 49). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.FUN.2016.4