Generalized intransitive dice: Mimicking an arbitrary tournament

A generalized \begin{document}$ N $\end{document}-sided die is a random variable id="M2">\begin{document}$ D $\end{document} on sample space of id="M3">\begin{document}$ equally likely outcomes taking values in the set positive integers. We say independent id="M4">\begin{document}$ sided dice id="M5">\begin{document}$ D_i, D_j that id="M6">\begin{document}$ D_i beats id="M7">\begin{document}$ $\end{document}, written id="M8">\begin{document}$ \to if id="M9">\begin{document}$ Prob(D_i > D_j) \frac{1}{2} $\end{document}. Examples are known intransitive id="M10">\begin{document}$ 6 dice, i.e. id="M11">\begin{document}$ D_1 D_2 D_3 but id="M12">\begin{document}$ A tournament size id="M13">\begin{document}$ n choice direction id="M14">\begin{document}$ i j for each edge complete graph id="M15">\begin{document}$ vertices. show id="M16">\begin{document}$ R id="M17">\begin{document}$ [n] = \{ 1, \dots, \} then sufficiently large id="M18">\begin{document}$ there exist sets id="M19">\begin{document}$ id="M20">\begin{document}$ D_1, D_n such id="M21">\begin{document}$ and only id="M22">\begin{document}$ id="M23">\begin{document}$