---
_id: '478'
abstract:
- lang: eng
text: '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.'
alternative_title:
- Frontiers in Artificial Intelligence and Applications
author:
- first_name: Krishnendu
full_name: Chatterjee, Krishnendu
id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87
last_name: Chatterjee
orcid: 0000-0002-4561-241X
- first_name: Rasmus
full_name: Ibsen-Jensen, Rasmus
id: 3B699956-F248-11E8-B48F-1D18A9856A87
last_name: Ibsen-Jensen
orcid: 0000-0003-4783-0389
citation:
ama: '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'
apa: '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'
chicago: '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.'
ieee: '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.'
ista: '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.'
mla: '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.'
short: K. Chatterjee, R. Ibsen-Jensen, in:, IOS Press, 2016, pp. 1432–1439.
conference:
end_date: 2016-09-02
location: The Hague, Netherlands
name: 'ECAI: European Conference on Artificial Intelligence'
start_date: 2016-08-29
date_created: 2018-12-11T11:46:41Z
date_published: 2016-01-01T00:00:00Z
date_updated: 2021-01-12T08:00:54Z
day: '01'
ddc:
- '004'
department:
- _id: KrCh
doi: 10.3233/978-1-61499-672-9-1432
file:
- access_level: open_access
checksum: 848043c812ace05e459579c923f3d3cf
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:07:59Z
date_updated: 2020-07-14T12:46:35Z
file_id: '4658'
file_name: IST-2018-950-v1+1_2016_Chatterjee_The_complexity.pdf
file_size: 2116225
relation: main_file
file_date_updated: 2020-07-14T12:46:35Z
has_accepted_license: '1'
intvolume: ' 285'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc/4.0/
month: '01'
oa: 1
oa_version: Published Version
page: 1432 - 1439
publication_status: published
publisher: IOS Press
publist_id: '7342'
pubrep_id: '950'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'The complexity of deciding legality of a single step of magic: The gathering'
tmp:
image: /images/cc_by_nc.png
legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode
name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
short: CC BY-NC (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 285
year: '2016'
...