The video explores what is believed to be the largest number ever used in a game, specifically within Magic: The Gathering, a complex card game with nearly 30,000 different cards and intricate interactions. Although the presenter does not play Magic, friends who do helped explain how certain cards can interact to produce extraordinarily large numbers. The game has rules to keep numbers manageable, such as only allowing whole integers and preventing infinite loops unless a player can stop them. Despite these regulations, a loophole involving three specific cards creates a scenario where the number of tokens generated grows at an astonishing rate.
The three key cards involved are simplified for explanation: Card A doubles the number of token copies entering play, Card B (called Astral Dragon or “make two”) creates two token copies of Card A, and Card C causes an extra token copy of Card B to appear when played. When combined, these cards create a feedback loop where tokens multiply exponentially. For example, playing Card B results in multiple copies of Card A being generated, which then double the incoming tokens repeatedly, leading to a rapid and massive increase in the number of tokens on the board.
This exponential growth results in numbers so large they quickly surpass everyday comprehension. The presenter calculates that after just a few iterations, the number of tokens reaches a figure with 22 digits, roughly 10^21, which would require an impractical amount of physical cards to represent—enough to fill millions of shipping containers. The sequence continues to grow even faster, forming a power tower of numbers 30 layers high, an unimaginably large but finite and exact number. This number is far beyond the total number of atoms in the observable universe, highlighting the sheer scale of the mathematical phenomenon occurring within the game.
Despite its enormity, this number is still finite and well-defined, unlike infinity. The presenter compares it to other famously large numbers like 52 factorial and Graham’s number, noting that while it is smaller than Graham’s number, it is an exact value directly arising from the game’s mechanics. However, due to the game’s rules, if a player cannot calculate the number exactly, it defaults to zero, meaning that in an official game setting, such a scenario might be disallowed or result in no tokens being counted. Nonetheless, this example stands as a fascinating intersection of mathematics and gaming, demonstrating how complex interactions can produce mind-bogglingly large numbers.
The video concludes by mentioning the sponsor, Jane Street, a research-driven trading firm that uses machine learning and neural networks in quantitative trading. They have created a neural network puzzle involving arranging 96 shuffled layers, which is a challenging problem related to factorial complexity. Viewers interested in deep mathematical and computational problems are encouraged to try the puzzle and explore Jane Street’s work. The presenter also thanks contributors who helped design the cards and inspired the video, inviting viewers to share other mathematical curiosities found in games.
