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On Solving an Aspect of Unfairness in the Tennis Doubles Scoring System

I this paper, we consider two identical (and equal) tennis pairs (or teams), (A1, A2) and (B1, B2). We assume player A1 is more effective on service than player A2 and player B1 more effective on service than B2. This is not an uncommon situation in doubles, particularly mixed doubles. We show that when two such identical tennis pairs play a single tiebreak set, the probability that (A1, A2) wins the set is not equal to the probability (B1, B2) wins the set and we conclude that, although the single tiebreak set is fair for singles, it is not fair for this situation in doubles. The advantage set is also unfair in this situation for some orders of serving. The scoring systems for doubles can be made fair by making small changes to the allowable winning scores, while maintaining the various other characteristics of tennis.