# All-play-all tournament design for 9 players

Julian D. A. Wiseman, February 2002

This 9-player all-play-all tournament design, last updated in February 2002, is based on an original by Dr Nicholas F. J. Inglis of The Department of Pure Mathematics and Mathematical Statistics at The University of Cambridge.

Available formats:
PDF (A4) Schedule, in score-sheet, with running totals; Blank score sheet, with running totals
PDF (A3) Schedule, in score-sheet, with running totals; Blank score sheet, with running totals
PDF (USL) Schedule, in score-sheet, with running totals; Blank score sheet, with running totals
Text Human-readable schedule, machine-readable schedule
Also see the all-play-all explanation and the links to designs for other numbers of players.

Properties of this tournament design:

 ``` Bye i ii iii iv 1 C F:G A:H B:I D:E 2 H E:I D:C A:G F:B 3 B G:D E:F H:C A:I 4 A C:F I:G E:B H:D 5 E B:H F:A I:D C:G 6 D I:C G:B F:H E:A 7 F D:A H:I G:E B:C 8 G H:E B:D C:A I:F 9 I A:B C:E D:F G:H ```
• Each player plays each of the others exactly once, and each player has one bye.

• No player plays two consecutive games at the same venue.

• Each player plays exactly once on each side of each venue.

• Hence each player plays twice at each venue, and each player plays four times on each side (left and right).

• It is seeded, so that important games come late in the tournament if player A is the best, B the second best, etc.

• It has a permutation score of 4107.9311069588284226484, which is maximal.

• It has a left-right asymmetry measure of 3.1597096245905773593, which is minimal given the assignment of games to rounds and venues.

Usual disclaimer and copyright terms apply.