English

The complexity of UNO

Discrete Mathematics 2013-12-03 v3 Computational Complexity

Abstract

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.

Keywords

Cite

@article{arxiv.1003.2851,
  title  = {The complexity of UNO},
  author = {Erik D. Demaine and Martin L. Demaine and Nicholas J. A. Harvey and Ryuhei Uehara and Takeaki Uno and Yushi Uno},
  journal= {arXiv preprint arXiv:1003.2851},
  year   = {2013}
}

Comments

13 body pages, 2 appendix pages, 1 table, 7 figures

R2 v1 2026-06-21T14:57:49.862Z