A team from MIT’s Hardness Group has demonstrated that certain levels in Super Mario are so complex that no program can always predict whether Mario can reach the end, placing the game itself in one of the most challenging classes of computational problems.
- Super Mario levels can be mathematically undecidable
- Research bridges classical gaming with complex computational theory
- Findings extend previous work by MIT Hardness Group on game complexity
What happened
Researchers affiliated with MIT’s Hardness Group explored the computational complexity of Super Mario, a classic video game involving navigating a platform-filled world to rescue Princess Peach. Using fan-created level editors alongside Super Mario Maker, four students created custom Mario levels so challenging that it is impossible to develop an algorithm that consistently determines whether Mario can complete these levels. This effectively categorizes these particular levels within the class of undecidable problems, a category far more complex than previously known.
This breakthrough builds on over a decade of work led by Erik Demaine, a MacArthur fellow and computer science professor, who has studied the computational hardness of video games. Previously, Super Mario was believed to be in PSPACE, a class where problems remain solvable but become impractical as they increase in size. The new results place it in the RE-Complete class, the highest known difficulty in the hierarchy, signifying fundamental limits to algorithmic prediction in gaming scenarios.
Why it matters
These findings highlight how classical video games like Super Mario can serve as rich models for exploring the boundaries of computation and complexity theory. The undecidability result implies no single computer program can predict the outcome of all possible game scenarios, analogous to foundational results like the Halting Problem established by Alan Turing in 1936.
Understanding these limits has broader implications beyond gaming, impacting fields such as cryptography, algorithm design, and artificial intelligence, where problem hardness defines what computers can or cannot solve efficiently. Moreover, this research underscores the educational and theoretical value of video games in computer science, relating entertainment to real-world computational challenges.
What to watch next
Future investigations will likely expand on other popular games to explore their computational boundaries, further linking recreational gaming with advanced theoretical concepts. The MIT Hardness Group may continue developing more complex levels to test the limits of computability and contribute to understanding undecidability in practical contexts.
Additionally, researchers may explore algorithmic heuristics or approximation methods applicable to these hard problems, seeking viable strategies for game-solving AI that work well in practice despite formal undecidability. This research may also influence game design by inspiring developers to craft puzzles with formally proven complexity characteristics.