Sicherman dice [wikipedia]

[mklabgr]

Sicherman dice are a famous pair of nonstandard six-sided dice discovered by mathematician George Sicherman in 1978. Instead of being numbered 1–6 on each die, one die has faces 1, 2, 2, 3, 3, 4 and the other 1, 3, 4, 5, 6, 8, yet together they produce exactly the same probability distribution for sums (2 through 12) as ordinary dice. 

They are remarkable because they are the only pair of six-sided dice labeled with positive integers that replicate the sum probabilities of standard dice while using different face values. The result is a classic example in combinatorics and probability, illustrating how different underlying structures can generate identical statistical outcomes. 

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