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Nontransitive dice are dice beating one another in a cyclic way: die A winsdie B, B wins C, and C wins A (like in a rock-paper-scissors game). In thisarticle, it has been shown that a structure of mutual wins of 3 nontransitivedice (with numbers equal to numbers from The Lo Shu magic square) can berepeated at least twice in different scales: - in the nontransitive relationsbetween three sets, each of which consists of three nontransitive dice (total 9dice); and - in the nontransitive relations between three sets, each of whichconsists of three nontransitive subsets, each of which consists of threenontransitive dice (total 27 dice). In other words, structures of nontransitivesuperiority relations can be self-similar. Aims of the future study can be: -to show opportunities for building self-similar structures of nontransitiverelations of arbitrary depths of nestedness; and - to design a recursivealgorithm of filling the structures with the appropriate numbers. Perhaps ageometrical presentation of these numbers forms a fractal structure.

Self-Similar Structures of Nontransitive Dice Sets: Examples of Nested "Rock-Paper-Scissors" Relations Based on Numbers from The Lo Shu Magic Square