On the distribution of winners’ scores in a round-robin tournament

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 correction-to-on-the-distribution-of-winners-scores-in-a-round-robin-tournament.pdf (166.82 KB)

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https://www.cambridge.org/core/journals/probability-in-the-engineering-and-informational-sciences/article/abs/on-the-distribution-of-winners-scores-in-a-roundrobin-tournament/6B7D2FC12A87CD0B685F21940C5D3646

Permanent Link

https://doi.org/10.1017/S0269964821000267
 http://hdl.handle.net/11603/30442

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

Author/Creator

Author/Creator ORCID

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

Date

2021-08-06

Type of Work

journal articles
preprints
Text

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Program

Citation of Original Publication

Malinovsky, Yaakov. “On the Distribution of Winners’ Scores in a Round-Robin Tournament.” Probability in the Engineering and Informational Sciences 36, no. 4 (October 2022): 1098–1102. https://doi.org/10.1017/S0269964821000267.

Rights

This article has been published in a revised form in Probability in the Engineering and Informational Sciences https://doi.org/10.1017/S0269964821000267. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © The Author(s), 2021. Published by Cambridge University Press.

Subjects

Abstract

In a classical chess round-robin tournament, each of 𝒏 players wins, draws, or loses a game against each of the other 𝒏 − 1 players. A win rewards a player with 1 points, a draw with ½ point, and a loss with 0 points. We are interested in the distribution of the scores associated with ranks of 𝒏 players after (ⁿ⁄₂) games, that is, the distribution of the maximal score, second maximum, and so on. The exact distribution for a general 𝒏 seems impossible to obtain; we obtain a limit distribution.