https://arxiv.org/abs/1904.09828 Skip to main content Cornell University We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate arxiv logo > cs > arXiv:1904.09828 [ ] Help | Advanced Search [All fields ] Search arXiv logo Cornell University Logo [ ] GO quick links * Login * Help Pages * About Computer Science > Artificial Intelligence arXiv:1904.09828 (cs) [Submitted on 24 Mar 2019 (v1), last revised 23 Apr 2019 (this version, v2)] Title:Magic: The Gathering is Turing Complete Authors:Alex Churchill, Stella Biderman, Austin Herrick Download a PDF of the paper titled Magic: The Gathering is Turing Complete, by Alex Churchill and 2 other authors Download PDF Abstract:$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit {Magic}$ is at least as hard as the Halting Problem, solving a problem that has been open for a decade. 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 result is also highly unusual in that all moves of both players are forced in the construction. This shows that even recognising who will win a game in which neither player has a non-trivial decision to make for the rest of the game is undecidable. We conclude with a discussion of the implications for a unified computational theory of games and remarks about the playability of such a board in a tournament setting. Subjects: Artificial Intelligence (cs.AI); Computational Complexity (cs.CC); Logic in Computer Science (cs.LO) Cite as: arXiv:1904.09828 [cs.AI] (or arXiv:1904.09828v2 [cs.AI] for this version) https://doi.org/10.48550/arXiv.1904.09828 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alex Churchill [view email] [v1] Sun, 24 Mar 2019 23:48:09 UTC (17 KB) [v2] Tue, 23 Apr 2019 10:16:57 UTC (458 KB) Full-text links: Access Paper: Download a PDF of the paper titled Magic: The Gathering is Turing Complete, by Alex Churchill and 2 other authors * Download PDF * PostScript * Other Formats (view license) Current browse context: cs.AI < prev | next > new | recent | 1904 Change to browse by: cs cs.CC cs.LO References & Citations * NASA ADS * Google Scholar * Semantic Scholar 3 blog links (what is this?) DBLP - CS Bibliography listing | bibtex Alex Churchill Stella Biderman Austin Herrick a export BibTeX citation Loading... BibTeX formatted citation x [loading... ] Data provided by: Bookmark BibSonomy logo Reddit logo (*) Bibliographic Tools Bibliographic and Citation Tools [ ] Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) [ ] Litmaps Toggle Litmaps (What is Litmaps?) [ ] scite.ai Toggle scite Smart Citations (What are Smart Citations?) ( ) Code, Data, Media Code, Data and Media Associated with this Article [ ] Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) [ ] DagsHub Toggle DagsHub (What is DagsHub?) [ ] Links to Code Toggle Papers with Code (What is Papers with Code?) [ ] ScienceCast Toggle ScienceCast (What is ScienceCast?) ( ) Demos Demos [ ] Replicate Toggle Replicate (What is Replicate?) [ ] Spaces Toggle Hugging Face Spaces (What is Spaces?) ( ) Related Papers Recommenders and Search Tools [ ] Link to Influence Flower Influence Flower (What are Influence Flowers?) [ ] Connected Papers Toggle Connected Papers (What is Connected Papers?) [ ] Core recommender toggle CORE Recommender (What is CORE?) * Author * Venue * Institution * Topic ( ) About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?) * About * Help * Click here to contact arXiv Contact * Click here to subscribe Subscribe * Copyright * Privacy Policy * Web Accessibility Assistance * arXiv Operational Status Get status notifications via email or slack