UNO Is Hard, Even for a Single Player

  • Erik D. Demaine
  • Martin L. Demaine
  • Ryuhei Uehara
  • Takeaki Uno
  • Yushi Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6099)


UNO\(\mbox{}^{\scriptsize\textregistered}\) is one of the world-wide well-known and popular card games. We investigate UNO from the viewpoint of combinatorial algorithmic game theory by giving some simple and concise mathematical models for it. They include cooperative and uncooperative versions of UNO, for example. As a result of analyzing their computational complexities, we prove that even a single-player version of UNO is NP-complete, while it becomes in P in some restricted cases. We also show that uncooperative two-player’s version is PSPACE-complete.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Erik D. Demaine
    • 1
  • Martin L. Demaine
    • 1
  • Ryuhei Uehara
    • 2
  • Takeaki Uno
    • 3
  • Yushi Uno
    • 4
  1. 1.MIT Computer Science and Artificial Intelligence LaboratoryCambridgeUSA
  2. 2.School of Information ScienceJAISTJapan
  3. 3.National Institute of InformaticsTokyoJapan
  4. 4.Graduate School of ScienceOsaka Prefecture UniversityJapan

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