May 6, 2026: Crazy Dice And The Boltzmann Distribution

Two economists recently wrote a paper proving the uniqueness of the Boltzmann Distribution - a specific formula used to describe probabilities in systems where things don't influence each other - using experiments featuring Crazy Dice. For 150 years, no one knew if this was the only distribution. Now we do. 

 

Crazy Dice, AKA Sicherman dice - invented in 1977 by Col. George Sicherman - are a pair of dice where one die in the pair has the numbers 1, 3, 4, 5, 6, 8, and the other has 1, 2, 2, 3, 3, 4, and when rolled together you get the same probability distribution of sums as a pair of normal dice (1,2,3,4,5,6). 

 

The economists realized that the Crazy Dice could be used as a great test of whether a formula can distinguish between independent and disguised-dependent systems, and they set out to see if they could find any other useful distributions. What they found instead was that only Boltzmann's theory works. You can read more about the paper and technical details here. 

 

Could Crazy Dice be useful for gaming? Since the sum distribution matches normal dice, you could swap them in for damage rolls, skill checks, ability scores, etc. If your dice have icons instead of numbers, there are some interesting possibilities: same success distribution, different icon mix, different feel. What would you use them for? Let us know on our forums, linked below!

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