The complexity of UNO

15 Mar 2010  ·  Erik D. Demaine, Martin L. Demaine, Nicholas J. A. Harvey, Ryuhei Uehara, Takeaki Uno, Yushi Uno ·

This paper investigates the popular card game UNO from the viewpoint of algorithmic combinatorial game theory. We define simple and concise mathematical models for the game, including both cooperative and uncooperative versions, and analyze their computational complexity. In particular, we prove that even a single-player version of UNO is NP-complete, although some restricted cases are in P. Surprisingly, we show that the uncooperative two-player version is also in P.

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Discrete Mathematics Computational Complexity G.2; F.1

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