# Brackets for tournament in a three player game

Suppose we have game which can only be played in a group of three.

I want my playing system to be somewhat similar to the "Double elimination tournament" but I have trouble getting my head around it.

I want the system to differentiate between the player which comes first and second in each match (or second and third respectively). For example I would like the winner to stay in the same bracket, the runner-up to move one bracket bellow and the looser to go to two brackets down.

I hope that this makes it at least a bit clear since I have scribbled over a ton of paper trying to come up with something that will work.

• What you are looking for sounds like you need a bunch of pre matches where you get seeded based on how you do in those. Commented Nov 15, 2017 at 22:30
• So you want to take track of the scores per match, so you eventually have a total game performance? Commented Nov 16, 2017 at 2:35

It's virtually identical to 2-player games, except there are two "loser" brackets instead of one, and an extra game could be needed because you can get into a situation where everyone lost twice.

``````________  \
________  ->01  ________  \
________  /                |
|
________  \                |
________  ->02  ________  ->16  ________  \
________  /                |               |
|               |
________  \                |               |
________  ->03  ________  /                |
________  /                                |
|
________  \                                |
________  ->04  ________  \                |
________  /                |               |
|               |
________  \                |               |
________  ->05  ________  ->17  ________  ->23  ________  -----------------\
________  /                |               |                               |
|               |                               |
________  \                |               |                               |
________  ->06  ________  /                |                               |
________  /                                |                               |
|                               |
________  \                                |                               |
________  ->07  ________  \                |                               |
________  /                |               |                               |
|               |                               |
________  \                |               |                               |
________  ->08  ________  ->18  ________  /                                |
________  /                |                                               |
|                                               |
________  \                |                                               |
________  ->09  ________  /                                                |
________  /                                                                |
|
|
__12P2__  \                |
|               |
__16P2__  \                |               |
__17P2__  ->19  ________  ->24  ________  ->26  ________
__18P2__  /                |               |
|               |
__01P2__  \                                |               |
__02P2__  ->10  ________  \                |               |
__03P2__  /                |               |               |
|               |               |
|               |               |
__04P2__  \                |               |               |
__05P2__  ->11  ________  ->20  ________  /                |
__06P2__  /                |                               |
|                               |
|                               |
__07P2__  \                |                               |
__08P2__  ->12  ________  /                                |
__09P2__  /                                                |
|
|
__12P3__  \                |
|               |
__16P3__  \                |               |
__17P3__  ->21  ________  ->25  ________  /
__18P3__  /                |
|
__01P3__  \                                |
__02P3__  ->13  ________  \                |
__03P3__  /                |               |
|               |
|               |
__04P3__  \                |               |
__05P3__  ->14  ________  ->22  ________  /
__06P3__  /                |
|
|
__07P3__  \                |
__08P3__  ->15  ________  /
__09P3__  /
``````

[`xxPy` refers to the person who placed in position `y` of in game `x`.]

• If `23P1` doesn't win 26, this is their first loss. Replay 26. [27]
• If `24P1` won 26 and `25P1` wins 27, everyone lost twice. Replay 27. [28]
• If `25P1` won 26 and `24P1` wins 27, everyone lost twice. Replay 27. [28]

An in-depth view of games 26..28:

``````                 Game Winner      Total Loss Count  Result
--------------   ----------------  ------------
26   27   28     23P1  24P1  25P1

Before game 26:                   0     1     1     => Game 26

After game 26:   23P1             0     2     2     => 23P1 wins
24P1             1     1     2     => Game 27
25P1             1     2     1     => Game 27

After game 27:   24P1 23P1        1     2     3     => 23P1 wins
24P1 24P1        2     1     3     => 24P1 wins
24P1 25P1        2     2     2     => Game 28

25P1 23P1        1     3     2     => 23P1 wins
25P1 24P1        2     2     2     => Game 28
25P1 25P1        2     3     1     => 25P1 wins

After game 28:   24P1 25P1 23P1   2     3     3     => 23P1 wins
24P1 25P1 24P1   3     2     3     => 24P1 wins
24P1 25P1 25P1   3     3     2     => 25P1 wins

25P1 24P1 23P1   2     3     3     => 23P1 wins
25P1 24P1 24P1   3     2     3     => 24P1 wins
25P1 24P1 25P1   3     3     2     => 25P1 wins
``````

Yes, that means the best players may have a chance of winning after being eliminated twice, but I don't think that's a problem, and I'm not sure there's a solution if it is.

• Look at curling's Page Playoff System as a possible resolution of the conflict. In that, four teams qualify for the playoff; 1 vs 2 is the first semi-final and 3 vs 4 is the quarter final; loser of 1 vs 2 and winner of 3 vs 4 play second semi-final. The Gold-medal and Bronze-medal games are winner take all single game matches. Various repechage systems exist in other games and sports also. Commented Nov 21, 2017 at 21:53
• @Forget I was ever here, there's already a way of handling 2-team games (and that's not it). This question is about 3-team games. Commented Nov 22, 2017 at 1:30
• Looking at your mid bracket the winner of game 12 goes to game 20 and then onto game 24. However the second place in game 12 seems to go straight through to game 24 unless I am misreading something... Commented Nov 27, 2017 at 17:43