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Tournament Designs: Carry-Over

Julian D. A. Wiseman, March 2002

Abstract: The best n teams from two all-play-all leagues go to a final which is all-play-all except that games already played are carried over. These pages describe optimised tournament designs for such carry-over finals.

Contents: Introduction; Presentations and file formats; Technical notes (permutation score; left-right asymmetry measure).

Publication history: Earlier versions of some of the designs here have previously been made available in paper form by Dr Nicholas F. J. Inglis, for the use of ETwA and CUTwC tournament organisers. This is believed to be the only publication on the web. Usual disclaimer and copyright terms apply.



Two leagues have played an all-play-all, and the top (say) eight teams from each league are to go through to a final. This final is to be a variant of an all-play-all. The scores from games between qualifying players are re-used; it remains only for each qualifier to play each of the other qualifiers whom they have not already opposed. So each qualifier plays each of the qualifiers from the other league. With eight teams going through this is done over eight rounds and at eight venues, with each team playing only once at each venue and only once in each round. On the right is the example in which eight teams from each league go to the final. Carry-over tournament designs are published for various numbers of players from 16+16=32 down to trivial sizes: 16+16=32, 15+15=30, 14+14=28, 13+13=26, 12+12=24, 11+11=22, 10+10=20, 9+9=18, 8+8=16, 7+7=14, 6+6=12, 5+5=10, 4+4=8, 3+3=6, 2+2=4 and 1+1=2. Also see the complete list of carry-over links.

The precise meaning of some of the terms can vary according to the game being played.

Presentations and file formats

Each of these carry-over tournaments is published in a number of different presentations and file formats.

Technical notes

There can be many ways to set out an carry-over tournament of any particular size. A particular one is chosen using some constraints and two optimisations.

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