Single-suit two-person card play
International Journal of Game Theory
The Othello game on an n × n board is PSPACE-complete
Theoretical Computer Science
Search in games with incomplete information: a case study using Bridge card play
Artificial Intelligence
Journal of the ACM (JACM)
Games, puzzles, and computation
Games, puzzles, and computation
GIB: imperfect information in a computationally challenging game
Journal of Artificial Intelligence Research
Generalized amazons is PSPACE-complete
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Improving state evaluation, inference, and search in trick-based card games
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Feature construction for reinforcement learning in hearts
CG'06 Proceedings of the 5th international conference on Computers and games
A skat player based on Monte-Carlo simulation
CG'06 Proceedings of the 5th international conference on Computers and games
UNO is hard, even for a single player
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
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Determining the complexity of perfect information trick-taking card games is a long standing open problem. This question is worth addressing not only because of the popularity of these games among human players, e.g., DOUBLE DUMMY BRIDGE, but also because of its practical importance as a building block in state-of-the-art playing engines for CONTRACT BRIDGE, SKAT, HEARTS, and SPADES. We define a general class of perfect information two-player trick-taking card games dealing with arbitrary numbers of hands, suits, and suit lengths. We investigate the complexity of determining the winner in various fragments of this game class. Our main result is a proof of PSPACE-completeness for a fragment with bounded number of hands, through a reduction from Generalized Geography. Combining our results with Wästlund's tractability results gives further insight in the complexity landscape of trick-taking card games.