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I think it would be pretty intuitive if we had red, green and blue dies for attack >> feint >> parry.

And in rpg d20, d12 and d10s are pretty common, so I think it could be tweaked for larger effect.

The challenge would be to make attributes matter in a non-binary and fair way (in the obvious d6+attribute vs d6+attribute system attributes only matter when they overcome the threshold).

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I have used genetic algorithms to search for non-transitive die triplets among the standard set of platonic dice, and exhaustively searched d6 and d8 numberings. If one insists that the advantage of A over B be the same as the advantage of B over C and C over A, then 61% is the best (farthest from 50%) that can be achieved for d6 and d8, and the best that I have been able to achieve for any larger dice.

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