The complexity of deciding legality of a single step of magic: The gathering

K. Chatterjee, R. Ibsen-Jensen, in:, IOS Press, 2016, pp. 1432–1439.

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Conference Paper | Published | English
Department
Series Title
Frontiers in Artificial Intelligence and Applications
Abstract
Magic: the Gathering is a game about magical combat for any number of players. Formally it is a zero-sum, imperfect information stochastic game that consists of a potentially unbounded number of steps. We consider the problem of deciding if a move is legal in a given single step of Magic. We show that the problem is (a) coNP-complete in general; and (b) in P if either of two small sets of cards are not used. Our lower bound holds even for single-player Magic games. The significant aspects of our results are as follows: First, in most real-life game problems, the task of deciding whether a given move is legal in a single step is trivial, and the computationally hard task is to find the best sequence of legal moves in the presence of multiple players. In contrast, quite uniquely our hardness result holds for single step and with only one-player. Second, we establish efficient algorithms for important special cases of Magic.
Publishing Year
Date Published
2016-01-01
Volume
285
Page
1432 - 1439
Conference
ECAI: European Conference on Artificial Intelligence
Conference Location
The Hague, Netherlands
Conference Date
2016-08-29 – 2016-09-02
IST-REx-ID

Cite this

Chatterjee K, Ibsen-Jensen R. The complexity of deciding legality of a single step of magic: The gathering. In: Vol 285. IOS Press; 2016:1432-1439. doi:10.3233/978-1-61499-672-9-1432
Chatterjee, K., & Ibsen-Jensen, R. (2016). The complexity of deciding legality of a single step of magic: The gathering (Vol. 285, pp. 1432–1439). Presented at the ECAI: European Conference on Artificial Intelligence, The Hague, Netherlands: IOS Press. https://doi.org/10.3233/978-1-61499-672-9-1432
Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. “The Complexity of Deciding Legality of a Single Step of Magic: The Gathering,” 285:1432–39. IOS Press, 2016. https://doi.org/10.3233/978-1-61499-672-9-1432.
K. Chatterjee and R. Ibsen-Jensen, “The complexity of deciding legality of a single step of magic: The gathering,” presented at the ECAI: European Conference on Artificial Intelligence, The Hague, Netherlands, 2016, vol. 285, pp. 1432–1439.
Chatterjee K, Ibsen-Jensen R. 2016. The complexity of deciding legality of a single step of magic: The gathering. ECAI: European Conference on Artificial Intelligence, Frontiers in Artificial Intelligence and Applications, vol. 285. 1432–1439.
Chatterjee, Krishnendu, and Rasmus Ibsen-Jensen. The Complexity of Deciding Legality of a Single Step of Magic: The Gathering. Vol. 285, IOS Press, 2016, pp. 1432–39, doi:10.3233/978-1-61499-672-9-1432.
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