The Importance of Rank in Trick-Taking Card Games
نویسندگان
چکیده
Recent years have seen a surge of interest in computational complexity results in card games. We focus in this paper on trick-taking card games, extending a study started in 2013. This class ranges from WHIST and CONTRACT BRIDGE to SKAT and TAROT. We investigate how the number of cards per suit, the ranks, impacts the complexity of solving arbitrary positions. We prove that 2 distinct ranks are sufficient to induce PSPACE-hardness for the question of determining if a team can make all tricks. This strengthens a 2013 result that assumed at least 5 cards per suit and no constraint on the number of tricks. Indeed, our analysis indicates that the concept of card discarding is expressive enough to encode universal quantification. Conversely, tractability ensues as soon as a second dimension is bounded. Our results provide a complete picture of the computational influence of the rank parameter.
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