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Mathematics

You can make fair dice from any shape you like

Want to roll an armadillo when you play Dungeons & Dragons, instead of standard dice? Now you can, thanks to a technique for mapping the probabilities produced by any shape

By Chris Stokel-Walker

28 May 2025

All of these strange-looking dice can produce a desired probability distribution

Keenan Crane

Gamers everywhere, rejoice: researchers have discovered that it is possible to transform any shape – from dragons to kittens – into a fair die, making it suitable for playing games that rely on random outcomes.

“We started from the idea of: ‘If you look at an object, can you tell its resting probabilities?’” says Keenan Crane at Carnegie Mellon University in Pittsburgh, Pennsylvania. In other words, if you roll a particular shape, what is the probability it lands in a particular orientation?

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