4 ms·
There's an assumption here that a polytope with equal area faces will be fair. I'd like to see a proof. My mathematical intuition is that the probability of st
by Syzygies 4y ago
There's an assumption here that a polytope with equal area faces will be fair. I'd like to see a proof.
My mathematical intuition is that the probability of stopping on a face depends on the extent that nearby faces slow a rotation, which depends on the angle of attack across each face. Without symmetry, this will vary by face.
- skykooler 4y agoThe article explicitly says that equal areas are not required for fairness; and gives this explanation for wanting equal areas: "Dice that are fair by symmetry (and hence under any reasonable throwing dynamics) always have to have an even number of sides and belong to certain symmetry groups (Diaconis & Keller 1989)."