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It turns out that you can make dice that beat each other according to any directed graph: https://math.stackexchange.com/questions/1624550/can-you-create-non-tr
by OscarCunningham 5y ago
It turns out that you can make dice that beat each other according to any directed graph: https://math.stackexchange.com/questions/1624550/can-you-create-non-transitive-dice-for-any-finite-graph https://math.stackexchange.com/questions/1624550/can-you-cre...
- messe 5y agoNote that by "dice" they are referring to any probability distribution the natural numbers (including those of infinite support), not just 6 sided dice.
- OscarCunningham 5y agoThe actual answer given at that link uses dice with a finite number of sides. In fact they all have an even number of sides, so you could make them physically with bipyramids or trapezohedra. https://en.wikipedia.org/wiki/Bipyramid https://en.wikipedia.org/wiki/Bipyramid https://en.wikipedia.org/wiki/Trapezohedron https://en.wikipedia.org/wiki/Trapezohedron