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It almost seems like you're expecting "exploding dice," which is where when you roll the max on one die. If you had to get values via exploding dice (eg if you could not roll the second die if you didn't roll a 0 aka 10 on the first die, and couldn't roll the third die if you didn't roll a 0 on the second die), then you'd be in a completely different ...


0

A die will have equal likelihood of each outcome if (a) each face has the same surface area and (b) the center of gravity of the actual die aligns with the center of the polyhedron. The reason dice have a set pattern for number faces (for example, in a D20 1 is opposite 20, and neighbor to 19, which is opposite 2, which in turn is neighbor to 18) is that if ...


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It is very easy to see if a die is fair, just see if you can deduce anything about the outcome without the faces. For example, a coin without faces is just a disc and a d6 without faces is just a cube. You can't tell anything from a resting cube or disc, so they are both fair. The same goes for all dice commonly used in rpg games. Technically a coin can ...


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Yes, d2, d3, d4, d6, d8, d10, d12, and d20 have uniform distributions Of these, the d4, d6, d8, d12, and d20 are regular polyhedrons. The d2 and d10 are not regular polyhedrons, but each face is nonetheless equally-likely.


15

Perfectly formed is a bit tricky, but yes. If a solid is rotationally symmetric such that one side being face up is the equivalent of any other side being face up, then there are no differences, and as such have the same probability. If you're interested in testing the fairness of real life dice, I'd suggest looking here: ...



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