Here at arceast, we don’t like doing single-elimination tournaments much. Sure, it’s nice and dramatic, but it often means a long journey for little action. And whilst that may be great if you can disappear off in half an hour to do something else, it rather defeats the whole participation objective.

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Each of the scenarios below makes the following assumptions (unless specified otherwise):

1. Each tournament has 16 players.
2. A seeding match lasts 1 song.
3. Non-seeding matches are best of 3.
4. Each result is just as likely. Therefore a best of 3 match lasts 2½ songs, as it assumes that a 2-0 win is just as likely as a 2-1 win.
5. A song takes 4 minutes to do. This might sound like a lot, but it allows a minute of head-scratching beforehand, two minutes of stomping, and a minute of organiser faffing.
6. There is always a third/fourth play-off in knockouts.

Each format is summarised as follows:

• Expected duration: how long the tournament is most likely to take
• Lower and upper bounds: how long the tournament could take in the best and worst case scenarios
• Play split: how many songs and matches each player would get, expressed as minimum/estimated/maximum number of songs.
• Advantages and disadvantages of the format
• Anything else noteworthy

Seeding into single-elimination KO

Expected duration: 48 songs in 3:12 (8 seeding songs, 8*2.5=20 last 16 songs, 4*2.5=10 quarter-final songs, 2*2.5 semi-final songs, 2.5 songs for 3rd, 2.5 songs for 1st)

Lower/upper bounds: 40 songs in 2:40 (8 seeding songs, then 32 KO songs) or 56 songs in 3:42 (8 seeding songs, then 48 KO songs)

Play split: 8 players get 1 song + 1 KO match (3/3.5/4 songs); 4 players get 1 song + 2 KO matches (5/6/7 songs);, 4 players get 1 song + 4 KO matches (9/11/13 songs).

Advantages: Easy to run, easy to understand.

Disadvantages: There’s a huge imbalance between the amount of playtime for the bottom half and the top four.

Notes: 32/40/48 songs is the spread for a single-elimination KO, which I’ll use a lot later.

Seeding into double-elimination KO

Expected duration: 81.75 songs in 5:27 (8 seeding songs; 37.5 single-elimination KO songs (due to no 3rd/4th place necessary); 2 sets of 4 loser QFs = 2*4*2.5=20 songs, 2 sets of 2 loser SFs = 2*2*2.5=10 songs, 2 sets of 2 loser finals = 2*1*2.5=5 songs, 1 winner v loser match = 2.5 songs, 1 possible rematch = 1.25 songs).

Lower/upper bounds: 66 songs in 4:24 (8 seeding songs, 30 single-elimination KO songs; 16 songs for loser QFs, 8 for loser SFs, 4 for loser finals, no rematch) or 98 songs in 6:32 (8 seeding songs, 45 KO songs, 24 loser QFs, 12 loser SFs, 6 loser Finals, plus a rematch of 3 songs.

Play split: Volatile due to extra matches in loser bracket. Weakest 4 players get 1 song + 2 KO matches (5/6/7 songs). Winner gets at least 1 song + 5 KO matches (11/13.5/16 songs) if no final rematch needed. Very possible some people play more than the winner does.

Advantages: Prevents one bad match ending the tournament.

Disadvantages: Long. Complicated. Tournament much longer and more complicated if persons 17 and 18 enter.

Notes: Tried this once with about 24 people and one dance machine. Nearly lost the will to live.

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Seeding, group phase, top 2 to KO phase

Expected duration: 80 songs in 5:20 (8 seeding; 4 groups of 6 matches = 4*6*2.5=60 songs; 20 songs for 8-man KO).

Lower/upper bounds: 64 songs in 4:16 (8 seeding, 4*12=48 group phase, 16 KO phase) or 96 songs in 6:24 (8 seeding, 4*18=72 group phase, 24 KO phase).

Play split: 8 players get 1 song + 3 group matches (7/8.5/10 songs); 4 players get 1 song + 3 group matches + 1 KO match (9/11/13 songs); 4 players get 1 song + 3 group matches + 3 KO matches (13/16/19 songs).

Advantages: All players get a decent number of songs.

Disadvantages: Gets complicated with 17-19 players as groups of 5 needed which can nearly double the group time.

Notes: Losers can also have their own bracket, as in Gold Rush Revolution. This adds 16/20/24 songs (1:04/1:20/1:36) to the tournament. Better than double-elimination in most ways for 2/4/8/16/32 etc fields.

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Modified Swiss

Expected duration: 100 songs in 6:40 (4 rounds of 8 matches = 4*8*2.5=80 songs; 20 songs for 8-man KO).

Lower/upper bounds: 80 songs in 5:20 (4*8*2=64 songs; 16 songs for 8-man KO) or 120 songs in 8:00 (4*8*3=96 songs; 24 songs for 8-man KO).

Play split: 8 players get 4 group matches (8/10/12 songs); 4 players get 4 group matches + 1 KO match (10/12.5/15 songs); 4 players get 4 group matches + 3 KO matches (14/17.5/21 songs).

Advantages: No seeding round (i.e. everyone getting bored of hearing the same song 8 times in a row). Everyone gets lots of songs, increasingly with players of their own ability. Two losses can still be enough to win the tournament.

Disadvantages: Difficult to follow, nightmare to manage without a computer. Not designed for events with one “table”!

Notes: Similar format to how Gold Rush +1 worked, except all went through to knockout. 2^n+1 players increases the time over 2^n players by a factor of about (n+2)/(n+1), for example 17 players take about 20% longer than 16, 33 players increases the already epic schedule by about 17%.