Magic: The Gathering is Turing Complete

@article{Churchill2021MagicTG,
  title={Magic: The Gathering is Turing Complete},
  author={Alexandrea Churchill and Stella Rose Biderman and Austin Herrick},
  journal={ArXiv},
  year={2021},
  volume={abs/1904.09828}
}
$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. [] Key Method To do this, we present a methodology for embedding an arbitrary Turing machine into a game of $\textit{Magic}$ such that the first player is guaranteed to win the game if and only if the Turing machine halts. Our result applies to how real $\textit{Magic}$ is played, can be achieved using standard-size tournament-legal decks, and does not rely on stochasticity or hidden information. Our…

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References

SHOWING 1-10 OF 14 REFERENCES
The Complexity of Deciding Legality of a Single Step of Magic: The Gathering
TLDR
The problem of deciding if a move is legal in a given single step of Magic is considered, and it is shown that the problem is coNP-complete in general; and in P if either of two small sets of cards are not used.
Games, puzzles and computation
TLDR
This thesis develops the idea of game as computation to a greater degree than has been done previously, and presents a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games.
Constraint Logic: A Uniform Framework for Modeling Computation as Games
  • E. Demaine, R. Hearn
  • Computer Science
    2008 23rd Annual IEEE Conference on Computational Complexity
  • 2008
TLDR
A simple game family, called constraint logic, where players reverse edges in a directed graph while satisfying vertex in-flow constraints is introduced, which makes it substantially easier to prove completeness of such games in their appropriate complexity classes.
The Frontier of Decidability in Partially Observable Recursive Games
TLDR
This paper proposes another criterion, the decidability of which is equivalent to the computability of approximately optimal play, and shows that this criterion is undecidable in the general case, but becomes decidable if the game halts almost surely whatever maybe the strategies of the players.
Monte Carlo search applied to card selection in Magic: The Gathering
  • C. D. Ward, P. Cowling
  • Computer Science
    2009 IEEE Symposium on Computational Intelligence and Games
  • 2009
TLDR
It is shown that Monte Carlo search is a promising avenue for generating a strong AI player for Magic: The Gathering and is examined with and without the use of a sophisticated rule-based approach to generate game rollouts.
Ensemble Determinization in Monte Carlo Tree Search for the Imperfect Information Card Game Magic: The Gathering
TLDR
This paper examines the use of Monte Carlo tree search (MCTS) for a variant of one of the most popular and profitable games in the world: the card game Magic: The Gathering, and examines the effect of utilizing various pruning strategies in order to increase the information gained from each determinization.
Cooperating in Video Games? Impossible! Undecidability of Team Multiplayer Games
We show the undecidability of whether a team has a forced win in a number of well known video games including: Team Fortress 2, Super Smash Brothers: Brawl, and Mario Kart.To do so, we give a
Playing Games with Algorithms: Algorithmic Combinatorial Game Theory
TLDR
Background in combinatorial game theory is reviewed, which analyzes ideal play in perfect-information games and results about the complexity of determining ideal play are surveyed, in terms of both polynomial-time algorithms and computational intractability results.
Classes of recursively enumerable sets and their decision problems
  • H. Rice
  • Mathematics, Computer Science
  • 1953
TLDR
This paper considers classes whose elements are re-cursively enumerable sets of non-negative integers whose properties are complete recursive enumerability and complete recursiveness.
Small Universal Turing Machines
...
1
2
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