{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/190409828","title":"Magic: The Gathering is Turing Complete","arxiv_id":"1904.09828","date":"2019-03-24","proceeding":null,"authors":["Alex Churchill","Stella Biderman","Austin Herrick"],"abstract":"$\\textit{Magic: The Gathering}$ is a popular and famously complicated trading\ncard game about magical combat. In this paper we show that optimal play in\nreal-world $\\textit{Magic}$ is at least as hard as the Halting Problem, solving\na problem that has been open for a decade. To do this, we present a methodology\nfor embedding an arbitrary Turing machine into a game of $\\textit{Magic}$ such\nthat the first player is guaranteed to win the game if and only if the Turing\nmachine halts. Our result applies to how real $\\textit{Magic}$ is played, can\nbe achieved using standard-size tournament-legal decks, and does not rely on\nstochasticity or hidden information. Our result is also highly unusual in that\nall moves of both players are forced in the construction. This shows that even\nrecognising who will win a game in which neither player has a non-trivial\ndecision to make for the rest of the game is undecidable. We conclude with a\ndiscussion of the implications for a unified computational theory of games and\nremarks about the playability of such a board in a tournament setting.","url_abs":"http://arxiv.org/abs/1904.09828v2","url_pdf":"http://arxiv.org/pdf/1904.09828v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"190409828","repo_url":"https://github.com/ChoKaPeek/UTMagic","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}