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Non-transitive Dice
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A set of 3 non-transitive dice.
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Model information
- Source
- Printables
- Category
- Math
- License
- Creative Commons — Attribution
A triplet of 20 mm Non-transitive Dice (see: https://en.wikipedia.org/wiki/Intransitive_dice) with sides:
- A: 1, 4, 4, 4, 4, 4
- B: 2, 2, 2, 5, 5, 5
- C: 3, 3, 3, 3, 3, 6
There are many known sets of non-transitive dice (see: https://singingbanana.com/dice/article.htm) but this particular set has the following properties:
- If you roll A against B:
- A wins 15/36 of the time.
- B wins 21/36 of the time.
- If you roll B against C,
- B wins 15/36 of the time.
- C wins 21/36 of the time.
- If you roll C against A,
- C wins 11/36 of the time.
- A wins 25/36 of the time.
Moreover, if you roll two copies of each dice, the dominance relationships are inverted:
- If you roll two copies of A against two copies of B:
- A+A wins 765/1296 of the time.
- B+B wins 531/1296 of the time.
- If you roll two copies of B against two copies of C:
- B+B wins 765/1296 of the time.
- C+C wins 531/1296 of the time.
- If you roll two copies of C against two copies of A:
- C+C wins 671/1296 of the time.
- A+A wins 625/1296 of the time.
I attach the parametric OpenScad file, so you can modify the design. It includes a module that allows you to create any cubic dice with pips ranging from 0 to 9.