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Bracket Diagrams for Different Numbers of Players and Eliminations

by Joe Czapski

Number of Players Double Elim. Triple Elim. Quadruple Elim.
3 2e3p 3e3p 4e3p
4 2e4p 3e4p 4e4p
5 2e5p 3e5p 4e5p
6 2e6p 3e6p 4e6p
7 2e7p 3e7p 4e7p
8 2e8p 3e8p 4e8p
9 2e9p 3e9p 4e9p
10 2e10p 3e10p 4e10p
11 2e11p 3e11p  
12 2e12p 3e12p 
13 2e13p 3e13p  
14 2e14p 3e14p  
15 2e15p 3e15p  
16 2e16p 3e16p  
17 2e17p 3e17p  
18 2e18p 3e18p  
19 2e19p 3e19p  
20 2e20p 3e20p  
21      
22 2e22p 3e22p  
23      
24      

Viewing the Tournament Brackets If You Don't Own Excel

The tournament brackets are XLS or XLSX files. If you don't own Excel, download and install the free Microsoft Excel app from the "app store" of your computer or mobile device.

Balanced Elimination Tournament Design

In the basic double and triple elimination formats that I've seen, there is a problem where the single player who comes out of the top (winner's) bracket does not play until a single opponent comes out of the bottom (loser's) bracket or brackets. With 8 players, the no-losses player skips 2 rounds of play in the double elimination tournament and 5 to 6 rounds of play in the triple elimination. Therefore, a player who loses his first one or two games must play several more games to get to the championship than the player who wins his first few games, and spectators are deprived of getting to see possibly the best player participate in the tournament as much as his opponents.

In an attempt to improve the situation with multiple-elimination tournaments, I designed these 'balanced' tournaments with these ideas:

  • Players with different numbers of losses can play each other at any point. That complicates the brackets because it's not always known ahead of time whether a loser moves on or is eliminated, but that issue can be handled neatly by using 'if necessary' games.
  • No player shall sit idle for more than one round consecutively.
  • Even out how often each player plays each other player as much as is practical. Avoid immediate replays.
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Correctness of the Tournament Bracket Diagrams

I've checked the diagrams for accuracy and playability, and on the triple and quadruple elimination diagrams I've run computer simulations. However, errors may remain. Before using one of these bracket diagrams for your tournament, you should run through it a few times on paper, flipping a coin for the result of each game. And you can run through it making a specific player always win or always lose. Please contact me if you find an error.

Contact: czaptournamentdesignorg

Last updated: 15 Mar 2018

About this Webpage

Since I put up this webpage in 2007, I've received a few dozen e-mails from people in several different countries who are using these tournament designs and from people interested in the design of tournaments. The formats have been used for billiards, backgammon, baseball, volleyball, table tennis, pinewood derby, RPG, and rock climbing tournaments. Some e-mails were critical and some had helpful suggestions.

From correspondance I've received, I see how important it is to tournament organizers to have formats accomdating any odd or even number of participants, depending on how many sign up ahead of time, or how many show up on the day of the tournament. I've posted brackets for every number of starting players from 3 to 20.

The brackets were originally PDF documents with a compact arrangement. Users requested Excel documents with the brackets spaced to allow player names to be typed in as the tournament progresses, so I replaced them with Excel versions. Another advantage of using Excel is that a user can change column width and text font and can print to fit any paper size or tiled sheets.

In the original tournament designs posted here, in the triple elimination designs, the last 2 or 3 rounds were made double elimination in order to simplify and prednisone shorten the brackets. In the double elimination designs, the final game was single elimination. This practice was criticized, I agreed with the criticism, and the designs now posted are purely double, triple, or quadruple elimination throughout.

I've received some criticism that, in certain situations in a late round of certain brackets, it is advantageous to lose a game in order to skip ahead to a later round. However, I believe that in practice it is never an advantage to lose a game in these kinds of elimination tournaments.

Boardgame Tournament

Boardgames are challenging to design a tournament for because there are up to six players per game and there are often ties for finishing order. I've developed an elimination design for boardgames that play well with 5, 4, or 3 players. And I've written a program that you can use as a tool to help run the tournament.

Tourneygeek.com Blog

by Dan Dabney

Read the many articles in Dan's blog. He digs into tournament philosophy, design, fairness and related subjects. Included are simulations and comparitive analyses of different 16 player double-elimination bracket designs including the one on this webpage.

Elimination Tournaments Requiring a Fixed Number of Wins

by Matthew Fayers

Read the paper: Fayers, M. "Multiple-elimination knockout tournaments with the fixed-win property" Discrete Mathematics 290 (2005) 89-97.

Improving the Double Elimination Tournament

by Jeff Soo

Visit the webpage: An Improved Double-Elimination Draw. Includes bracket diagrams.

Designing a Tournament

by Tony Bowes

Read the articles: Designing a Tournament and A Grading System for Comparing Tournament Structures