Hanabi is NP-complete, Even for Cheaters who Look at Their Cards

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

Thumbnail PDF


  • Filesize: 0.54 MB
  • 17 pages

Document Identifiers

Author Details

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

Cite AsGet BibTex

Jean-Francois Baffier, Man-Kwun Chiu, Yago Diez, Matias Korman, Valia Mitsou, André van Renssen, Marcel Roeloffzen, and Yushi Uno. Hanabi is NP-complete, Even for Cheaters who Look at Their Cards. In 8th International Conference on Fun with Algorithms (FUN 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 49, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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).
  • algorithmic combinatorial game theory
  • sorting


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Antoine Bauza. Hanabi. URL: http://www.antoinebauza.fr/?tag=hanabi.
  2. BoardGameGeek. URL: https://boardgamegeek.com/boardgame/98778/hanabi.
  3. Alex Churchill. Magic: The gathering is Turing complete. Unpublished manuscript available at http://www.toothycat.net/~hologram/Turing/index.html.
  4. Christopher Cox, Jessica De Silva, Philip Deorsey, Franklin H. J. Kenter, Troy Retter, and Josh Tobin. How to make the perfect fireworks display: Two strategies for Hanabi. Mathematics Magazine, 88(5):323-336, 2015. Google Scholar
  5. Erik D. Demaine. Personal communication. Google Scholar
  6. Erik D. Demaine. Playing games with algorithms: Algorithmic combinatorial game theory. CoRR, cs.CC/0106019v2, 2008. Google Scholar
  7. Erik D. Demaine, Martin L. Demaine, Nicholas J. A. Harvey, Ryuhei Uehara, Takeaki Uno, and Yushi Uno. UNO is hard, even for a single player. Theor. Comp. Sci., 521:51-61, 2014. Google Scholar
  8. Spiel des Jahres award. URL: http://www.spieldesjahres.de/en/hanabi.
  9. Aviezri S. Fraenkel and David Lichtenstein. Computing a perfect strategy for n x n chess requires time exponential in n. J. Comb. Theory, Ser. A, 31(2):199-214, 1981. Google Scholar
  10. Martin Gardner. Mathematical Games: The Entire Collection of His Scientific American Columns. The Mathematical Association of America, 2005. Google Scholar
  11. Robert Hearn and Erik D. Demaine. Games, Puzzles, and Computation. A. K. Peters, 2009. Google Scholar
  12. Michael Lampis and Valia Mitsou. The computational complexity of the game of set and its theoretical applications. In 11^th Latin American Symposium, pages 24-34. Springer, 2014. Google Scholar
  13. Kenichiro Nakai and Yasuhiko Takenaga. NP-completeness of pandemic. JIP, 20(3):723-726, 2012. Google Scholar
  14. Hirotaka Osawa. Solving Hanabi: Estimating hands by opponent’s actions in cooperative game with incomplete information. In AAAI workshop: Computer Poker and Imperfect Information, pages 37-43, 2015. Google Scholar