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Documents authored by Churchill, Alex

Document
DOI: 10.4230/LIPIcs.FUN.2024.31
A Programming Language Embedded in Magic: The Gathering

Authors: Howe Choong Yin and Alex Churchill

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

Abstract
Previous work demonstrated that the trading card game Magic: The Gathering is Turing complete, by embedding a universal Turing machine inside the game. However, this is extremely hard to program, and known programs are extremely inefficient. We demonstrate techniques for disabling Magic cards except when certain conditions are met, and use them to build a microcontroller with a versatile programming language embedded within a Magic game state. We remove all choices made by players, forcing all player moves except when a program instruction asks a player for input. This demonstrates Magic to be at least as complex as any two-player perfect knowledge game, which we demonstrate by supplying sample programs for Nim and the Collatz conjecture embedded in Magic. As with previous work, our result applies to how real Magic is played, and can be achieved using a tournament-legal deck; but the execution is far faster than previous constructions, generally one cycle of game turns per program instruction.
Cite as

Howe Choong Yin and Alex Churchill. A Programming Language Embedded in Magic: The Gathering. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 31:1-31:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{yin_et_al:LIPIcs.FUN.2024.31,
  author =	{Yin, Howe Choong and Churchill, Alex},
  title =	{{A Programming Language Embedded in Magic: The Gathering}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{31:1--31:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.31},
  URN =		{urn:nbn:de:0030-drops-199391},
  doi =		{10.4230/LIPIcs.FUN.2024.31},
  annote =	{Keywords: Programming, computability theory, Magic: the Gathering, two-player games, tabletop games}
}
Document
DOI: 10.4230/LIPIcs.FUN.2021.9
Magic: The Gathering Is Turing Complete

Authors: Alex Churchill, Stella Biderman, and Austin Herrick

Published in: LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020)

Abstract
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 Magic is at least as hard as the Halting Problem. This provides a positive answer to the question "is there a real-world game where perfect play is undecidable under the rules in which it is typically played?", a question that has been open for a decade [David Auger and Oliver Teytaud, 2012; Erik D. Demaine and Robert A. Hearn, 2009]. To do this, we present a methodology for embedding an arbitrary Turing machine into a game of 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 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.
Cite as

Alex Churchill, Stella Biderman, and Austin Herrick. Magic: The Gathering Is Turing Complete. In 10th International Conference on Fun with Algorithms (FUN 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 157, pp. 9:1-9:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{churchill_et_al:LIPIcs.FUN.2021.9,
  author =	{Churchill, Alex and Biderman, Stella and Herrick, Austin},
  title =	{{Magic: The Gathering Is Turing Complete}},
  booktitle =	{10th International Conference on Fun with Algorithms (FUN 2021)},
  pages =	{9:1--9:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-145-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{157},
  editor =	{Farach-Colton, Martin and Prencipe, Giuseppe and Uehara, Ryuhei},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.9},
  URN =		{urn:nbn:de:0030-drops-127706},
  doi =		{10.4230/LIPIcs.FUN.2021.9},
  annote =	{Keywords: Turing machines, computability theory, Magic: the Gathering, two-player games}
}
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