  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.
