X amount of teams, 4 players per team

[DaveTheMaori]

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]

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]

Thanks for replying

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]

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.

[Ian Wakeling]

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 p8

1  A1 C2 E3 G4 J1 L2 N3 P4
1  A2 C1 E4 G3 J2 L1 N4 P3
1  A3 C4 E1 G2 J3 L4 N1 P2
1  A4 C3 E2 G1 J4 L3 N2 P1
1  B1 D2 F3 H4 I1 K2 M3 O4
1  B2 D1 F4 H3 I2 K1 M4 O3
1  B3 D4 F1 H2 I3 K4 M1 O2
1  B4 D3 F2 H1 I4 K3 M2 O1

2  A1 C3 F1 H3 J2 L4 M2 O4
2  A2 C4 F2 H4 J1 L3 M1 O3
2  A3 C1 F3 H1 J4 L2 M4 O2
2  A4 C2 F4 H2 J3 L1 M3 O1
2  B1 D3 E1 G3 I2 K4 N2 P4
2  B2 D4 E2 G4 I1 K3 N1 P3
2  B3 D1 E3 G1 I4 K2 N4 P2
2  B4 D2 E4 G2 I3 K1 N3 P1

3  A1 C4 F3 H2 I2 K3 N4 P1
3  A2 C3 F4 H1 I1 K4 N3 P2
3  A3 C2 F1 H4 I4 K1 N2 P3
3  A4 C1 F2 H3 I3 K2 N1 P4
3  B1 D4 E3 G2 J2 L3 M4 O1
3  B2 D3 E4 G1 J1 L4 M3 O2
3  B3 D2 E1 G4 J4 L1 M2 O3
3  B4 D1 E2 G3 J3 L2 M1 O4

4  A1 D1 F2 G2 J4 K4 M3 P3
4  A2 D2 F1 G1 J3 K3 M4 P4
4  A3 D3 F4 G4 J2 K2 M1 P1
4  A4 D4 F3 G3 J1 K1 M2 P2
4  B1 C1 E2 H2 I4 L4 N3 O3
4  B2 C2 E1 H1 I3 L3 N4 O4
4  B3 C3 E4 H4 I2 L2 N1 O1
4  B4 C4 E3 H3 I1 L1 N2 O2

5  A1 D2 F4 G3 I4 L3 N1 O2
5  A2 D1 F3 G4 I3 L4 N2 O1
5  A3 D4 F2 G1 I2 L1 N3 O4
5  A4 D3 F1 G2 I1 L2 N4 O3
5  B1 C2 E4 H3 J4 K3 M1 P2
5  B2 C1 E3 H4 J3 K4 M2 P1
5  B3 C4 E2 H1 J2 K1 M3 P4
5  B4 C3 E1 H2 J1 K2 M4 P3

6  A1 D3 E2 H4 I3 L1 M4 P2
6  A2 D4 E1 H3 I4 L2 M3 P1
6  A3 D1 E4 H2 I1 L3 M2 P4
6  A4 D2 E3 H1 I2 L4 M1 P3
6  B1 C3 F2 G4 J3 K1 N4 O2
6  B2 C4 F1 G3 J4 K2 N3 O1
6  B3 C1 F4 G2 J1 K3 N2 O4
6  B4 C2 F3 G1 J2 K4 N1 O3

7  A1 D4 E4 H1 J3 K2 N2 O3
7  A2 D3 E3 H2 J4 K1 N1 O4
7  A3 D2 E2 H3 J1 K4 N4 O1
7  A4 D1 E1 H4 J2 K3 N3 O2
7  B1 C4 F4 G1 I3 L2 M2 P3
7  B2 C3 F3 G2 I4 L1 M1 P4
7  B3 C2 F2 G3 I1 L4 M4 P1
7  B4 C1 F1 G4 I2 L3 M3 P2

8  A1 C1 E1 G1 I1 K1 M1 O1
8  A2 C2 E2 G2 I2 K2 M2 O2
8  A3 C3 E3 G3 I3 K3 M3 O3
8  A4 C4 E4 G4 I4 K4 M4 O4
8  B1 D1 F1 H1 J1 L1 N1 P1
8  B2 D2 F2 H2 J2 L2 N2 P2
8  B3 D3 F3 H3 J3 L3 N3 P3
8  B4 D4 F4 H4 J4 L4 N4 P4