# All-play-all tournament design for 10 players

Julian D. A. Wiseman, February 2002

This 10-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
Also see the all-play-all explanation and the links to designs for other numbers of players.

Properties of this tournament design:

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

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

• Each player plays at most once on any one side of any venue.

• Hence each player plays twice at four venues and once at one venue, and each player plays four times on one side (left or right) and five on the other (right or left).

• 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 4107.8420807221827999456, which is maximal.

• It has a left-right asymmetry measure of 3.3081785399344925125, which is minimal given the assignment of games to rounds and venues.

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