Round Robin Tournament Scheduling

### X amount of teams, 4 players per team

DaveTheMaori · 5 · 3210

#### DaveTheMaori

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• Posts: 2
on: June 04, 2014, 02:09:19 AM
Hello and thank you for reading my post

I'm running a Poker Tournament where teams of 4 players each, compete over "3 rounds of play". During these "3 rounds of play" each player would play another player (from another team) only once and never play against someone from their own team. I have already figured out a schedule if there were 12 teams, 14 teams, 15 teams and 16 teams. However, 13 teams (a prime number) seems to be more difficult. I also haven't been able to figure out how to run a Tournament if there is an amount of teams that is not 12, 14, 15 or 16. But, thanks to this website, I now have a schedule for 4 teams.

I ask if you can please help me figure out a mathematical formula for an unknown amount of teams, 4 players per team, where players compete against others only once and never against their own team mates.

Thanks again for reading this post
DaveTheMaori

#### Ian Wakeling

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Reply #1 on: June 04, 2014, 08:08:39 AM
Hi Dave,

I am not certain about the format of play.  Perhaps you can show us your 14 team schedule, how many poker games are there in a round, how many players in each game, how many byes (if any).

Thanks,

Ian.

#### DaveTheMaori

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• Posts: 2
Reply #2 on: June 06, 2014, 03:18:02 AM

Attached is a Schedule for 14 teams of 4 players per team with a starting stack of chips (3,000). In this schedule of 8 Tables, these players play poker on their tables' until only one person has all the chips on their respective table, then that round will end. The next "round of play" will begin where everyone will start again with the same starting amount (3,000) and play again until only one person from each table has all the chips. Then they will play again in "Round Three" until one person on each table will have all the chips.

I have figured out a points scheme so that each player will receive points for their team dependant on where they place during each "round of play". Then the total amount of points for each team will be calculated to find an overall winning team.

As you'll see, there are no byes and no team has any advantage or disadvantage over another team because they always play against the same amount of people every time. It would be easy for me to simply take a team off but then some tables would have 7 players and some tables would have 6 players. This would give an advantage to the players on a table of 6 and a disadvantage to the players on a table of 7.

Thanks again for reading my post
DaveTheMaori

#### Ian Wakeling

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Reply #3 on: June 06, 2014, 10:26:39 AM
Thanks for the extra details and for the schedule, I understand now.  So for 16 teams of 4 there are 8 tables of 8 players?  The problem of 13 being a prime number leaves you only two possible choices,  you could play 13 games of 4 players each per round, or you must have byes, and for the latter I think you would need to have 13 rounds in order to give everyone the same number of games.  I am guessing both these options may not be appropriate, so for 13 teams, your proposal to drop a team from the 14 round schedule may be your only practical option.
« Last Edit: June 06, 2014, 10:28:21 AM by Ian »

#### Ian Wakeling

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Reply #4 on: June 07, 2014, 11:28:09 AM
If there are 16 teams (A to P) of 4 you might consider the schedule below.  It does meet your criteria, and no pair of players play together twice even if you use all 8 rounds.  But note that team A members never oppose B, C never oppose D, etc...   A bonus is that you could remove the last column and have a schedule for the 14 teams (A to N).

`r  p1 p2 p3 p4 p5 p6 p7 p81  A1 C2 E3 G4 J1 L2 N3 P41  A2 C1 E4 G3 J2 L1 N4 P31  A3 C4 E1 G2 J3 L4 N1 P21  A4 C3 E2 G1 J4 L3 N2 P11  B1 D2 F3 H4 I1 K2 M3 O41  B2 D1 F4 H3 I2 K1 M4 O31  B3 D4 F1 H2 I3 K4 M1 O21  B4 D3 F2 H1 I4 K3 M2 O12  A1 C3 F1 H3 J2 L4 M2 O42  A2 C4 F2 H4 J1 L3 M1 O32  A3 C1 F3 H1 J4 L2 M4 O22  A4 C2 F4 H2 J3 L1 M3 O12  B1 D3 E1 G3 I2 K4 N2 P42  B2 D4 E2 G4 I1 K3 N1 P32  B3 D1 E3 G1 I4 K2 N4 P22  B4 D2 E4 G2 I3 K1 N3 P13  A1 C4 F3 H2 I2 K3 N4 P13  A2 C3 F4 H1 I1 K4 N3 P23  A3 C2 F1 H4 I4 K1 N2 P33  A4 C1 F2 H3 I3 K2 N1 P43  B1 D4 E3 G2 J2 L3 M4 O13  B2 D3 E4 G1 J1 L4 M3 O23  B3 D2 E1 G4 J4 L1 M2 O33  B4 D1 E2 G3 J3 L2 M1 O44  A1 D1 F2 G2 J4 K4 M3 P34  A2 D2 F1 G1 J3 K3 M4 P44  A3 D3 F4 G4 J2 K2 M1 P14  A4 D4 F3 G3 J1 K1 M2 P24  B1 C1 E2 H2 I4 L4 N3 O34  B2 C2 E1 H1 I3 L3 N4 O44  B3 C3 E4 H4 I2 L2 N1 O14  B4 C4 E3 H3 I1 L1 N2 O25  A1 D2 F4 G3 I4 L3 N1 O25  A2 D1 F3 G4 I3 L4 N2 O15  A3 D4 F2 G1 I2 L1 N3 O45  A4 D3 F1 G2 I1 L2 N4 O35  B1 C2 E4 H3 J4 K3 M1 P25  B2 C1 E3 H4 J3 K4 M2 P15  B3 C4 E2 H1 J2 K1 M3 P45  B4 C3 E1 H2 J1 K2 M4 P36  A1 D3 E2 H4 I3 L1 M4 P26  A2 D4 E1 H3 I4 L2 M3 P16  A3 D1 E4 H2 I1 L3 M2 P46  A4 D2 E3 H1 I2 L4 M1 P36  B1 C3 F2 G4 J3 K1 N4 O26  B2 C4 F1 G3 J4 K2 N3 O16  B3 C1 F4 G2 J1 K3 N2 O46  B4 C2 F3 G1 J2 K4 N1 O37  A1 D4 E4 H1 J3 K2 N2 O37  A2 D3 E3 H2 J4 K1 N1 O47  A3 D2 E2 H3 J1 K4 N4 O17  A4 D1 E1 H4 J2 K3 N3 O27  B1 C4 F4 G1 I3 L2 M2 P37  B2 C3 F3 G2 I4 L1 M1 P47  B3 C2 F2 G3 I1 L4 M4 P17  B4 C1 F1 G4 I2 L3 M3 P28  A1 C1 E1 G1 I1 K1 M1 O18  A2 C2 E2 G2 I2 K2 M2 O28  A3 C3 E3 G3 I3 K3 M3 O38  A4 C4 E4 G4 I4 K4 M4 O48  B1 D1 F1 H1 J1 L1 N1 P18  B2 D2 F2 H2 J2 L2 N2 P28  B3 D3 F3 H3 J3 L3 N3 P38  B4 D4 F4 H4 J4 L4 N4 P4`
« Last Edit: June 07, 2014, 11:31:00 AM by Ian »