# Carry-Over tournament design for 10+10=20 players

Julian D. A. Wiseman, March 2002

This is a carry-over tournament design for 10+10=20 players. It therefore assumes that two qualifying leagues (called ‘Roman’ and ‘Italic’) have played an all-play-all, and that the top 10 players from each are through to the final. In the final these 20 players are then to play each other, except that games already played between them are ‘carried over’. The players in the Roman league are called A, B, C, etc, and those in the Italic league a, b, c, etc.

It was last updated in March 2002, and is based on an original 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 carry-over explanation and the links to similar designs for other numbers of players.

Properties of this tournament design:

i ii iii iv v vi vii viii ix x E:e D:i j:B F:b a:H A:g I:d h:G J:c C:f g:F C:j d:G c:E D:h I:e A:i J:a B:f H:b D:f H:d b:J h:A B:g F:a E:j e:C i:G c:I B:i e:A E:h j:H f:J c:D C:g I:b F:d G:a H:c f:I a:D i:C j:F G:b J:e d:A E:g B:h J:d G:g i:F I:a b:E C:h f:H c:B e:D A:j b:C a:E A:f g:J I:i d:B G:c D:j H:h e:F j:G h:J g:I e:B c:A i:H b:D F:f a:C d:E h:I F:c H:e f:G d:C J:j a:B E:i b:A g:D A:a B:b C:c D:d G:e f:E h:F g:H j:I i:J
• Each player plays exactly once each of the players in the other league.

• Each player plays exactly once at each venue.

• Each player plays five times on each side (left and right).

• It is seeded, so that important games come late in the tournament. It is assumed that player A is better than B, etc, and that a is better than b, etc. (Usually rankings are determined by the players’ scores in the qualifying rounds.)

• It has a permutation score of 7164.6949407478632565471, which is either maximal or near-maximal.

• It has a left-right asymmetry measure of 3524497/6350400 = 0.55500394, which is minimal.

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