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A specific example

Posted By: Timothy Chow
Date: Monday, 26 September 2016, at 2:12 a.m.

In Response To: OT - Tennis Tournament Format Question (Rick Janowski)

Here's a specific way to implement your first suggestion. [A,B] means that Team A plays Team B.

Round 1: [1,2] and [3,4] and [5,6]
Round 2: [1,4] and [2,5] and [3,7]
Round 3: [1,5] and [2,6] and [4,7]
Round 4: [1,7] and [3,6] and [4,5]
Round 5: [2,3] and [6,7]

This way, every team gets one bye, and plays 4 of the 6 remaining teams. So there is no need to compensate for byes.

In some sense this is the best you can do. Ideally, everyone would play everyone else, but that requires 21 matches, and in five rounds you can play at most 15 matches. If you eliminate only 6 of the 21 matches, then there's no way to ensure that every team plays the same number of matches, and then you'd have to come up with some awkward way of compensating for the imbalance.

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