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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
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    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)
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