A generalized $ N $-sided die is a random variable $ D $ on a sample space of $ N $ equally likely outcomes taking values in the set of positive integers. We say of independent $ N $-sided dice $ D_i, D_j $ that $ D_i $ beats $ D_j $, written $ D_i \to D_j $, if $ Prob(D_i > D_j) > \frac{1}{2} $. A collection of dice $ \{ D_i : i = 1, \dots, n \} $ models a tournament on the set $ [n] = \{ 1, 2, \dots, n \} $, i.e. a complete digraph with $ n $ vertices, when $ D_i \to D_j $ if and only if $ i \to j $ in the tournament. By using regular $ n $-fold partitions of the set $ [Nn] $ to label the $ N $-sided dice we can model an arbitrary tournament on $ [n] $ and $ N $ can be chosen to be less than or equal to $ N = 3^{n-2} $.
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