Geodesic
Two game-set inequalities
Journal of integer sequences, Tome 6 (2003) no. 4
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.
Classification : 60C05
Keywords: games, inequalities, probability, sets 
@article{JIS_2003__6_4_a2,
     author = {Shur,  Walter},
     title = {Two game-set inequalities},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {4},
     zbl = {1064.05004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a2/}
}
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Shur,  Walter. Two game-set inequalities. Journal of integer sequences, Tome 6 (2003) no. 4. http://geodesic.mathdoc.fr/item/JIS_2003__6_4_a2/