Rocket League 20 Player Switch Doubles Round Robin

[sc0ttr0berts0n]

Hi all, I'm so grateful to have found a place that understands this stuff. I've been largely on my own with this issue, but as my league has grown, the math is getting too complex for my brute force program to solve it by happen stance.

I believe what I have is a Switch Double Round Robin tournament. Here are the constraints:

Player count: 20
Partner with each individual once, (forming 20*19/2 = 190 teams)
190 teams then are split into 95 Matches
Winner is player with most wins after 95 matches, and their 19 games.


The big question: I would love to know if its possible for each player to play each *other* player an equal amount of times.

I can make plenty of seasons, but the deviation between the minimum and maximum about of times a player sees another player is too great. I would love it to be equal across the whole league.

Any insight or research would be helpful. Terms to google, solutions. etc.

I've written a program in typescript to generate my seasons, if seeing it is helpful:
https://github.com/sc0ttr0berts0n/diet-league-season-generator/blob/master/src/index.ts
https://github.com/sc0ttr0berts0n/diet-league-season-generator/blob/master/src/season.ts

Here is an example of a "perfect" 4 man seasons given my criteria:

Players:
ABCD

Teams:
AB AC AD
BC BD
CD

Matches:
AB CD
AC BD
AD BC

Thank you all very much. --Scott

[Ian Wakeling]

Hi Scott,

What you are describing has been studied mathematically.  A balanced doubles tournament schedule is possible where each player partners each other player exactly once, and opposes each other player exactly twice.  It is easy to show that a necessary condition for such a schedule to exist is that there are either 4n players , or 4n+1 players,  for some integer n>=1. Proving that they all exist is harder, but has been done.  Search for 'whist tournament design' on Google Scholar to start uncovering the literature on this.  There is a book by Anderson if you want to get into the combinatorial math.

Schedules for 4n can be found on this site (click above on 'pages that inspired this forum' and then 'whist tables').  Bill Butler has a huge web page on these schedules (examples for 4n+1 from about a third of the way down).

Hope that helps,

Ian

[sc0ttr0berts0n]

Ian, Thanks a ton! My group has a few coders in it and we crunched it last night and got a solution. Thank you so much. We've been chasing this problem for about 18 months on our own.