Verified 5 October 2026. A new computer-science preprint argues that Riftbound: League of Legends Trading Card Game can simulate a universal Turing machine. That does not mean a normal match secretly runs software, nor that the construction is a competitive deck recommendation. It means the game’s rules and card interactions are expressive enough, under a carefully prepared board state and a prescribed strategy, to reproduce a general model of computation.
The paper, Riftbound is Turing Complete, was posted to arXiv on 27 September 2026 by Nathan Dalaklis and Beckett Fields of the University of Oklahoma. The authors call their construction Jayce’s Computer.
What “Turing complete” means here
A universal Turing machine is an abstract computer capable of simulating any other Turing machine when it receives the appropriate program and input. In a card-game proof, cards, tokens, zones, ready or exhausted states and repeatable actions stand in for the tape, symbols, states and transitions of that machine.
The authors build a seven-state, four-symbol machine—written UTM(7,4)—through legal sequences of Riftbound game states. Their main theorem says that deciding whether a game-state-directed strategy wins during one Riftbound turn is undecidable. In plain language: there is no general algorithm that can always inspect every such constructed position and tell whether that prescribed turn will eventually finish with a win.
How Jayce’s Computer is assembled
The construction uses Jayce, Defender of Tomorrow as its Legend and relies on a network of gear, units and spells. Among the named pieces are Jayce, Brilliant Inventor, Hextech Formula, Platewyrm Egg, Acceleration Gate, Questionable Tome, Garbage Grabber, Hextech Anomaly, Ancient Henge and Profiteer.
Very roughly, the deck first creates the draw and resource loops needed to keep acting. Mech and Sprite tokens then encode tape cells and symbols. Ready, exhausted and empowered states record machine state, while repeated plays implement transitions. For a halting state, the paper uses Renata Glasc, Mastermind and Heimerdinger, Inventor to turn the simulated halt into repeated scoring; a reject state can instead be represented by drawing from an empty deck.
The authors calculate quadratic string-card complexity: encoding an input of length k requires O(k2) cards played. Most of the construction and the computation occur on Jayce’s fifth turn once the required setup has been reached.
The important limits
This is a mathematical existence proof, not a robust tournament combo. The paper assumes that the opponent follows a suitable scoring tempo and does not disrupt Jayce’s base, spells, movement or scoring. If the position is interrupted, the prescribed strategy may fail. The authors explicitly note that their result is weaker than the earlier Magic: The Gathering construction because Riftbound does not force every opposing action.
The paper describes its decks as tournament-legal at the time of writing. Legality is still date-sensitive. Riot’s official Rules Hub lists the current Constructed bans and was last updated for legality on 18 September 2026. A future ban, erratum or rule change could invalidate one route without disproving the broader idea that another construction may exist.
Why this matters beyond the puzzle
The result highlights how open-ended Riftbound’s action phase can become when card draw, recycling, readying, resource generation and token state all interact. It also creates a precise bridge between TCG rules engineering and theoretical computer science: the interesting claim is not “this combo is infinite,” but that a family of valid game states can represent arbitrary computation.
For players, the practical lesson is more modest. Complex loops must still be demonstrated with exact card text, legal game states and interruption windows. The paper is a fascinating stress test of the rules, not permission to shortcut a sequence at an event without explaining it.
If you are learning the current card pool rather than building a computer out of it, our Riftbound Radiance mechanics guide covers Deploy, Show Off and Disarm with a much more practical focus.
