If you’ve ever played a sport like racquetball, you know how tough it can be to beat someone with a great serve.
But what if the rules were changed and the person who lost the point got to serve?
Well, if both players were equally as a good, you’d get longer and more competitive games without altering the chances of the first server winning the match, according to new research done by a group that includes Math Department Research Associate Walter Stromquist.
Stromquist and his colleagues published their findings in the paper, "Catch-Up: A Rule that Makes Service Sports More Competitive.” The paper’s co-authors are Steve Brams of NYU, Marc Kilgour of WIlfrid Laurier Univeristy, and Mehmet Ismail of Maastricht University.
Stromquist first heard about his colleagues’ interest in the “Catch-Up Rule” at a game-theory meeting at Dagstuhl, in Germany, last summer.
Ismail told those attending the meeting that all of his experiments showed that the catch-up rule gave the same game-winning probability as the standard rule, and he found this surprising, but his group hadn’t yet been able to prove it. Stromquist, was able to provide the proof.
“I think somebody should try it, perhaps in school events,” says Stromquist of the catch-up rule. “Perhaps people will like it and it will catch on.”
The researchers also consider two “trailing rules” that make the server the player who trails in total score.
Interestingly, they found that the one rule that would make purposefully losing a point advantageous was a trailing rule that, in the case of a tie, gives the serve to the player who was trailing prior to the tie.
Stromquist has taught Game Theory at Bryn Mawr as a visiting professor.