UNO is hard, even for a single player

Authors:
Erik D. Demaine;Martin L. Demaine;Ryuhei Uehara;Takeaki Uno;Yushi Uno
Affiliations:
MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA;School of Information Science, JAIST, Nomi, Ishikawa, Japan;National Institute of Informatics, Tokyo, Japan;Graduate School of Science, Osaka Prefecture University, Sakai, Japan
Venue:
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Year:
2010

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Abstract

UNO® 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.