UNO Is Hard, Even for a Single Player
نویسندگان
چکیده
This paper investigates the popular card game UNO R © 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.
منابع مشابه
The complexity of UNO
This paper investigates the popular card game UNOR © 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....
متن کاملUNO Gets Easier for a Single Player
This work is a follow up to [2, FUN 2010], which initiated a detailed analysis of the popular game of UNO R ©. We consider the solitaire version of the game, which was shown to be NP-complete. In [2], the authors also demonstrate a n ) algorithm, where c is the number of colors across all the cards, which implies, in particular that the problem is polynomial time when the number of colors is a ...
متن کاملSports Result Prediction Based on Machine Learning and Computational Intelligence Approaches: A Survey
In the current world, sports produce considerable statistical information about each player, team, games, and seasons. Traditional sports science believed science to be owned by experts, coaches, team managers, and analyzers. However, sports organizations have recently realized the abundant science available in their data and sought to take advantage of that science through the use of data mini...
متن کاملNew Heuristic Algorithms for Solving Single-Vehicle and Multi-Vehicle Generalized Traveling Salesman Problems (GTSP)
Among numerous NP-hard problems, the Traveling Salesman Problem (TSP) has been one of the most explored, yet unknown one. Even a minor modification changes the problem’s status, calling for a different solution. The Generalized Traveling Salesman Problem (GTSP)expands the TSP to a much more complicated form, replacing single nodes with a group or cluster of nodes, where the objective is to fi...
متن کاملGame Refinement Theory and Multiplayer Games: Case Study Using UNO
Game refinement theory has started to provide some interesting tools to measure sophistication of board games, sport games, and video games. In this paper, we apply game refinement theory to UNO R © card game, from which we identify valuable aspects regarding multiplayer and incomplete information game. Specifically, we analyze game refinement value zone of UNO and reveal recommended number of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Theor. Comput. Sci.
دوره 521 شماره
صفحات -
تاریخ انتشار 2010