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.