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

Jean-Francois Baffier, Man Kwun Chiu, Yago Diez, Matias Korman, Valia Mitsou, André van Renssen, Marcel Roeloffzen, Yushi Uno

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

6 Citations (Scopus)
113 Downloads (Pure)


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
EditorsE.D. Demaine, F. Grandoni
Place of PublicationDagstuhl
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Number of pages17
ISBN (Electronic)9783959770057
Publication statusPublished - 1 Jun 2016
Externally publishedYes
Event8th International Conference on Fun with Algorithms (FUN 2016) - La Maddalena, Italy
Duration: 8 Jun 201610 Jun 2016
Conference number: 8

Publication series

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


Conference8th International Conference on Fun with Algorithms (FUN 2016)
Abbreviated titleFUN 2016
CityLa Maddalena


  • Algorithmic combinatorial game theory
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