# 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… Expand

## 19 Citations

Magic: the Gathering is as Hard as Arithmetic

- MathematicsArXiv
- 2020

It is shown that the ``mate-in-$n$'' problem for Magic is $\Delta^0_n$-hard and that optimal play in two-player Magic is non-arithmetic in general.

Baba is You is Undecidable

- Computer ScienceArXiv
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This work establishes the undecidability of 2019 puzzle game Baba is You through a reduction from the Post correspondence problem introduced by Neary (STACS 2015) that is limited to pairs of words.

Recursed is not Recursive: A Jarring Result

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- Computer ScienceArXiv
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It is proved that three strategy video games from the Sid Meier’s Civilization series are Turing complete by building three universal Turing machines–one for each game–using only the elements present in the games, and using their internal rules and mechanics as the transition function.

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This work proposes a strategy-based framework for basic decision making in Magic: The Gathering and describes procedures and provides experimental evidence for the effectiveness of this approach.

Exceptional Gestalt Mining: Combining Magic Cards to Make Complex Coalitions Thrive

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It is argued that EGM can be deployed on datasets from sports where several roles exist that directly interact in play, such as ice hockey, and found combinations of cards that jointly work better in multicolor decks than in decks employing fewer colors.

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- Computer Science
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The conceptual esolangs offer the most direct challenge to the definition of programming language, a commonly used term which is surprisingly unspecific, and usually understood through utility, despite the fact that programming languages predate digital computers.

Reinforcement Learning in Collectible Card Games: Preliminary Results on Legends of Code and Magic

- Computer Science
- 2019

This paper proposes a pure reinforcement learning approach to the card game Legends of Code and Magic, in contrast to search strategies, most commonly used in this domain.

Architecture for a multilingual Wikipedia

- Computer ScienceArXiv
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This paper proposes an architecture for a system that fulfills the goal in two parts: creating and maintaining content in an abstract notation within a project called Abstract Wikipedia, and creating an infrastructure called Wikilambda that can translate this notation to natural language.

Architecture for a multilingual Wikipedia

- Computer Science
- 2020

This paper proposes an architecture for a system that fulfills the goal in two parts: creating and maintaining content in an abstract notation within a project called Abstract Wikipedia, and creating an infrastructure called Wikilambda that can translate this notation to natural language.

## References

SHOWING 1-10 OF 14 REFERENCES

The Complexity of Deciding Legality of a Single Step of Magic: The Gathering

- MathematicsECAI
- 2016

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

- Philosophy
- 2006

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

- Computer Science2008 23rd Annual IEEE Conference on Computational Complexity
- 2008

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

- EconomicsInt. J. Found. Comput. Sci.
- 2012

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

- Computer Science2009 IEEE Symposium on Computational Intelligence and Games
- 2009

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

- Computer ScienceIEEE Transactions on Computational Intelligence and AI in Games
- 2012

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

- Computer ScienceFUN
- 2018

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

- Computer ScienceMFCS
- 2001

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

- Mathematics, Computer Science
- 1953

This paper considers classes whose elements are re-cursively enumerable sets of non-negative integers whose properties are complete recursive enumerability and complete recursiveness.