Angel, Levi; Davis, Matt Properties of sets of nontransitive dice with few sides. (English) Zbl 1390.05039 Involve 11, No. 4, 643-659 (2018). Summary: We define and investigate several properties that sets of nontransitive dice might have. We prove several implications between these properties, which hold in general or for dice with few sides. We also investigate some algorithms for creating sets of 3-sided dice that realize certain tournaments. Cited in 1 Document MSC: 05B30 Other designs, configurations 05C20 Directed graphs (digraphs), tournaments 60C05 Combinatorial probability Keywords:nontransitive dice; probability; tournaments PDF BibTeX XML Cite \textit{L. Angel} and \textit{M. Davis}, Involve 11, No. 4, 643--659 (2018; Zbl 1390.05039) Full Text: DOI OpenURL References: [1] 10.1002/jcd.21563 · Zbl 1377.05073 [2] ; Bednay, Proceedings of the 8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications, 15 (2013) [3] ; Bozóki, Miskolc Math. Notes, 15, 39 (2014) [4] 10.1038/scientificamerican1270-110 [5] 10.2307/2974903 · Zbl 0808.05011 [6] 10.4169/college.math.j.48.1.10 · Zbl 1443.97048 [7] ; Steinhaus, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 7, 67 (1959) [8] 10.4064/am-5-4-321-332 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.