2022/01/13 by Malinovsky, Yaakov
#05C20 #62G32 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2201.05018
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 1/2 point, and a loss with 0 points. We are interested in the distribution of the scores associated with ranks of n players after n \choose 2 games, i.e. 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.