A Scheme to Generate Pairing for n Players in a Round Robin Tournament

Article by How-Hie Ling (h.ling@qut.edu.au)

I came up with the following scheme in 1982 for generating pairings for for N players in a round robin competition. It has been used in some regional football competitions.

The scheme works as follows:

  1. In the the first row, list out the player (or team) numbers in sequential order.
  2. If the largest number is odd, add the next number (the ghost player) to make even.
  3. Keep the the last number fixed at the last column.
  4. For subsequent rows, rotate the numbers to the right (except the last number) until the rotation is complete.
  5. Apply the pairing rainbows which arch from the first to the last, the second to the second last, and so on.
  6. Write out the pairs.
  7. The player who matches up with the ghost player has a bye.

Here is a simple example for 4 players. The rows of numbers are the result of applying steps 1 to 4. The rainbows at the top are the pairing operators (step 5).

1 2 3 4
3 1 2 4
2 3 1 4

Reading out the pairing gives:

round 1 1-4 2-3
round 2 3-4 1-2
round 3 2-4 3-1

The Game Cabinet - editor@gamecabinet.com - Ken Tidwell