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 → D j , if P rob(D i > D j) > 1 2. A collection of dice {D i : i = 1,. .. , n} models a tournament on the set [n] = {1, 2,. .. , n}, i.e. a complete digraph with n vertices, when D i → D j if and only if i → j in the tournament. By using regular n-fold partitions of the set [N n] 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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