Malinovsky, YaakovMoon, John W.2022-10-132022-10-132024-04-16https://doi.org/10.48550/arXiv.2208.14932http://hdl.handle.net/11603/26168Richard 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.13 pagesen-USThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.Text