UNO Is Hard, Even for a Single Player

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 U...

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Bibliographic Details
Published inFun with Algorithms Vol. 6099; pp. 133 - 144
Main Authors Demaine, Erik D., Demaine, Martin L., Uehara, Ryuhei, Uno, Takeaki, Uno, Yushi
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2010
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Online AccessGet full text
ISBN9783642131219
3642131212
ISSN0302-9743
1611-3349
DOI10.1007/978-3-642-13122-6_15

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Summary: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.
Bibliography:Original Abstract: UNO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mbox{}^{\scriptsize\textregistered}$\end{document} 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.
ISBN:9783642131219
3642131212
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-13122-6_15