Round Robin Tournament Scheduling

20 person switch round robin 6 rounds

AmandaK · 2 · 1092

AmandaK

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on: October 17, 2023, 11:29:23 PM
Hi!  I'm hosting a 20 person round robin switch partners each round..  Would like to have different partner each round and only face the  same opponent 1, maybe 2 times in the rounds.  6 rounds ideally on 5 courts...is this doable without playing the same people multiple times? 

I've tried many different ways and it keeps coming out playing the same opponents, i.e duplicate opponent happens multiple times in the 6 rounds.

Desperate for any advice, my brain hurts.lol.


Ian Wakeling

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Reply #1 on: October 29, 2023, 08:07:30 AM
Unfortunately it is known that the perfect 6 round schedule, where all players meets with 18 different people (6 as partners and 12 as opponents) does not exist. It's worth pointing out that the perfect 5 round schedule does exist - use the "20 golfers play in foursomes" schedule from Ed Pegg's page and assign the foursomes to 2 vs 2 any way you like.

For 6 rounds, a player's partners can be all different and their opponents all different, but there may be overlap between the two groups, in other words some pairs of players meet twice, once as partners and once as opponents.  The most interesting schedule I can find with this property is as follows:

( 3  7 v 14 12)  ( 1 11 v 17 20)  (18 16 v  9 15)  (10 19 v 13  8)  ( 5  2 v  6  4)
(15 20 v 12  2)  ( 1  6 v 19  3)  ( 4 17 v 18 13)  ( 7 10 v  9 11)  (14  5 v  8 16)
(11 15 v  4  8)  ( 7 18 v  5 20)  (12  3 v 13 19)  ( 1 14 v  2  9)  (17  6 v 16 10)
( 7 13 v 15  6)  (19 11 v  2 16)  ( 5  3 v  9 17)  (20  4 v 10 14)  (18  1 v 12  8)
(12 19 v  9  4)  (11  6 v 18 14)  ( 2  8 v  7 17)  ( 5 10 v  1 15)  (20 16 v 13  3)
( 9  6 v 20  8)  (15 19 v 14 17)  ( 5 11 v 13 12)  (18  2 v 10  3)  (16  1 v  7  4)

Above the players are one of two types:
Type 1 - pairs of players from the subset {3,12,13,19} are all on court together twice - once as partners and once as opponents.  So a type 1 player is on court together with a total of 15 different people.

Type 2 - players from the subset {1,2,4,5,6,7,8,9,10,11,14,15,16,17,18,20} meet 18 different players. So type 2 players experience optimal mixing.

I think this it the best schedule in the sense of having the greatest possible number of Type 2 players.