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Server advantage in tennis matches

Part of: Markov processes Game theory

Published online by Cambridge University Press:  14 July 2016

I. M. MacPhee ,
Jonathan Rougier  and
G. H. Pollard
I. M. MacPhee*
Affiliation:
University of Durham
Jonathan Rougier*
Affiliation:
University of Durham
G. H. Pollard*
Affiliation:
University of Canberra
*
∗ Postal address: Department of Mathematical Sciences, University of Durham, Science Site, South Road, Durham DH1 3LE, UK
∗ Postal address: Department of Mathematical Sciences, University of Durham, Science Site, South Road, Durham DH1 3LE, UK
∗∗∗ Postal address: School of Information Sciences and Engineering, University of Canberra, Belconnen, ACT 2601, Australia
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Abstract

We show that the advantage that can accrue to the server in tennis does not necessarily imply that serving first changes the probability of winning the match. We demonstrate that the outcome of tie-breaks, sets and matches can be independent of who serves first. These are corollaries of a more general invariance result that we prove for n-point win-by-2 games. Our proofs are non-algebraic and self-contained.

Keywords

Tennistie-breakn-point win-by-k games

MSC classification

Primary: 91A60: Probabilistic games; gambling 91A05: 2-person games
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1182 - 1186
Copyright
Copyright © Applied Probability Trust 2004 

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