Sicherman dice
Only non-standard dice with same sum distribution as normal dice.
Sicherman dice are a pair of six-sided dice that break from the standard numbering. One die has faces showing 1, 2, 2, 3, 3, and 4, while the other shows 1, 3, 4, 5, 6, and 8. Their claim to fame is that they are the only six-sided dice that are not standard, use only positive integers, and still produce the exact same odds for each possible sum as a regular pair of dice. George Sicherman, from Buffalo, New York, came up with them in 1978.
- inventor
- George Sicherman
- location
- Buffalo, New York
- year_invented
- 1978
- field
- Mathematics
- known_for
- Sicherman dice
- type
- Pair of six-sided dice with non-standard numbers
Lore & Background
Sicherman dice were discovered by George Sicherman of Buffalo, New York and were originally reported by Martin Gardner in a 1978 article in Scientific American. The numbers can be arranged so that all pairs of numbers on opposing sides sum to equal numbers, 5 for the first die and 9 for the second. Later, in a letter to Sicherman, Gardner mentioned that a magician he knew had anticipated Sicherman's discovery.
Reader's Guide
Sicherman dice are a significant mathematical curiosity because they are the only pair of six-sided dice that are not standard (1–6 on each die) yet produce exactly the same frequency of sums as a normal pair. This property makes them a classic example in combinatorics and generating functions. The dice were discovered by George Sicherman and publicized by Martin Gardner in 1978. Their generating function factorization shows that the polynomial for a standard die can be factored and reassigned to produce the same sum distribution. While the sum distribution matches, other properties differ: for example, the probability of rolling doubles is 1/6 with regular dice but 1/9 with Sicherman dice. The discovery has been generalized to more than two dice and non-cubical dice by later mathematicians. Sicherman dice remain a popular puzzle and teaching tool in probability and number theory.
Did You Know?
- Sicherman dice are the only pair of six-sided dice that are not normal, bear only positive integers, and have the same probability distribution for the sum as normal dice.
- The probability of rolling doubles with Sicherman dice is 1/9, compared to 1/6 with regular dice.
- The numbers on opposing sides of Sicherman dice sum to 5 for the first die and 9 for the second.
- Martin Gardner reported that a magician he knew had anticipated Sicherman's discovery.
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