Papers for

computational theorists

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Riftbound card game can simulate any computer with legal decks

Riftbound is Turing Complete

Abstract: Riftbound: League of Legends Trading Card Game is a trading card game about capturing and holding locations in a king-of-the-hill style contest. Originally released in China in August of 2025, and later released in the United States in October of 2025, the game has been well received for its depth and complexity. In this paper we demonstrate a facet of this complexity by providing sequences of valid game states which construct Universal Turing machines within the game. Each of these machines are constructed with tournament legal decks at the time of writing and strategies assigned are directed by the game state. We also show that given an appropriate board state the machine may be constructed and the computation may be performed in one game turn.

Sun 27 SeptComputational Complexity

The gist

Some games are more complex than they seem, and this card game called Riftbound is one of them. The authors show you can set up the pieces and use legal decks to simulate a completely universal computer inside the game. This means, within the rules and one turn, the game can perform any calculation a computer can, given the right setup. It highlights unexpected depth in the game’s design and complexity.

Open → 2609.33839v1