Round Robin Tournament Scheduling

Tri-ball (3 teams playing simultaneously)

ndodge · 5 · 3402

ndodge

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on: August 12, 2017, 11:45:19 PM
Tri-ball is a volleyball variant where 3 teams are playing at the same time (there are three nets separating the 3 teams).

I may have a situation where I have 7 teams, and I was hoping to have 7 rounds, such that each team played 3 times, and opposed each other team once.  I'm realizing this is hard to do by hand, and I'm rusty at programming at the moment, so I thought I'd see if a solution was easily made by someone else.

Thank you,
Nathan


ndodge

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Reply #1 on: August 13, 2017, 12:06:41 AM
If that proves quite easy to solve, an added request is that the 4 teams that are sitting out play each other, in two games, in normal volleyball, so that each team gets 4 games of regular volleyball in addition to the 3 games of triball, with the four regular games ideally against different opponents.


Ian Wakeling

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Reply #2 on: August 13, 2017, 03:59:39 AM
Nathan,

The solution for the tri-ball games is known as The Fano Plane, so there is no need for any programming.

Here is a schedule with the extra 4 games of regular volleyball per team:

(1 2 4)  (3 6)  (5 7)
(2 3 5)  (4 7)  (6 1)
(3 4 6)  (5 1)  (7 2)
(4 5 7)  (6 2)  (1 3)
(5 6 1)  (7 3)  (2 4)
(6 7 2)  (1 4)  (3 5)
(7 1 3)  (2 5)  (4 6)


Regards,

Ian
« Last Edit: August 13, 2017, 04:00:09 AM by Ian »


ndodge

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Reply #3 on: August 13, 2017, 08:47:30 PM
Thank you, that is an interesting math aspect.  That schedule would work well in some cases.  However, what I was hoping to do was to include triball as part of a day of many events, with triball as a sampling of events during a main portion, and was hoping to have 3 teams playing triball 3 of the rounds while a lot of other events are going on, so that 5 teams would get to play it once, and 2 teams would play it twice (i.e., using up the 9 team spots for 3 rounds of triball).  I was using letters for teams, and in respective rounds when triball was going on, the teams were ABC, DEF, GAD in my initial schedule (i.e., A and D play twice, everyone else once).  I was then planning on doing a triball after-event, and if all teams wanted in, I would take the 3 rounds that had already been done, and do four more rounds, so that each had played triball three times in total, and score the 7 total rounds.  However, when I look at the Fano plane solution, I can't seem to pick three initial rounds such that 5 play once and 2 play twice.  To get everyone to play at least once, I seem to have to pick a combo of 3 rows such that 1 team is in all 3 rows.

I'm wondering if I want to have the 7 round property that each team plays 3 times, against different opponents, if I have to accept that in the first 3 of those rounds, to get everyone to play at least once in those 3 rounds, that 1 team will have played all 3 rounds.  If so, I'll have to think about it.


Ian Wakeling

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Reply #4 on: August 14, 2017, 03:03:16 AM
You are correct, that one of the teams must play 3 times in the 3 initial rounds if you want to be able to complete the tri-ball tournament later on.  Using the geometrical analogy from the link, this is a consequence of the fact that any pair of lines meet at exactly one point.