|Journal of Integer Sequences, Vol. 6 (2003), Article 03.4.1|
Abstract: Two players compete in a contest where the first player to win a specified number of points wins the game, and the first player to win a specified number of games wins the set. This paper proves two generalized inequalities, each independent of the probability of winning a point, concerning the better player's chances of winning. Counterexamples are given for two additional conjectured inequalities. A sequence of integers which plays a significant role in this paper can be found in A033820 of the On-line Encyclopedia of Integer Sequences.
(Concerned with sequence A033820.)
Received July 29 2003; revised version received November 24 2003. Published in Journal of Integer Sequences December 6 2003.