All-play-all tournament design for 7 players

Julian D. A. Wiseman, February 2002

This 7-player all-play-all tournament design, last updated in February 2002, is based on originals by Matt Fayers of The Department of Mathematics at Queen Mary, University of London (formerly 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:

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

• Most players do not play two consecutive games at the same venue, the exceptions being A and B, each of which plays at the same venue either side of their respective byes.

• All play three times on each side (left and right).

• All except A and B play twice at each venue; A playing three times at iii and only once at ii, and B three times at ii and once at iii.

• 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 1298.6453055654608306213, which is maximal given only two players with these properties of A and B.

• It has a left-right asymmetry measure of 0.9946938775510205666, which is minimal given the assignment of games to rounds and venues.

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