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Expected length and probability of winning a tennis game

Published online by Cambridge University Press:  13 October 2021

Curtis Cooper  and
Robert E. Kennedy
Curtis Cooper
Affiliation:
School of Computer Science and Mathematics, University of Central Missouri, Warrensburg, MO 64093, USA, e-mail: cooper@ucmo.edu
Robert E. Kennedy
Affiliation:
School of Computer Science and Mathematics, University of Central Missouri, Warrensburg, MO 64093, USA, e-mail: kennedy233@gmail.com
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Extract

The game of tennis has provided mathematicians with many interesting problems. In [1], the problem of finding the probability that a certain player wins a tennis tournament was studied. Gale [2] determined the best serving strategy in tennis. First, we assume Alice and Bob play a game of tennis using the standard (or Deuce/Ad) scoring system, without a tiebreaker, and that Alice serves the game. We also assume that the probability that Alice wins any point she serves is . Stewart [3] proved that the probability that Alice wins is

$${{15{p^4} - 34{p^5} + \;28{p^6} - 8{p^7}} \over {1 - 2p\; + \;2{p^2}}}$$
.

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 564 , November 2021 , pp. 490 - 500
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Copyright
© The Mathematical Association 2021

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References

Cooper, C., A knockout tournament problem, Crux Mathematicorum, 8 (1982) pp. 93-96.Google Scholar
Gale, D., Optimal strategy for serving in tennis, Mathematics Magazine, 44 (1971) pp. 197-199.CrossRefGoogle Scholar
Stewart, I., Game, set and math, Dover (2007).Google Scholar
Cooper, C. and Kennedy, R. E., A generating function for the distribution of the scores of all possible bowling games, Mathematics Magazine, 63 (1990) pp. 239-243.Google Scholar