On Round-Robin Tournaments with a Unique Maximum Score

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2208.14932v5.pdf (201.87 KB)

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https://arxiv.org/abs/2208.14932

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https://doi.org/10.48550/arXiv.2208.14932
 http://hdl.handle.net/11603/26168

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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https://orcid.org/0000-0003-2888-674X

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2024-04-16

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journal articles
preprints
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Abstract

Richard Arnold Epstein (1927-2016) published the first edition of "The Theory of Gambling and Statistical Logic" in 1967. He introduced some material on round-robin tournaments (complete oriented graphs) with n labeled vertices in Chapter 9; in particular, he stated, without proof, that the probability that there is a unique vertex with the maximum score tends to 1 as n tends to infinity. Our object here is to give a proof of this result along with some historical remarks and comments.