On round-robin tournaments with a unique maximum score

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ajc_v89_p024.pdf (173.52 KB)

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https://ajc.maths.uq.edu.au/pdf/89/ajc_v89_p024.pdf

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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

Date

2024

Type of Work

journal articles
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Citation of Original Publication

Malinovsky, Yaakov, and John W Moon. “On Round-Robin Tournaments with a Unique Maximum Score.” AUSTRALASIAN JOURNAL OF COMBINATORICS 89, no. 1 (2024): 24–31. https://ajc.maths.uq.edu.au/pdf/89/ajc_v89_p024.pdf

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Attribution 4.0 International

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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 goal here is to give a proof of this result along with some historical remarks and comments.