Could someone tell me the formula for determining the number of rounds in a double elimination tournament?

Question

Christ Almighty, does anyone remember when the web was marginally HELPFUL instead of a bee-line straight to an endless cycle of repeating ads from people trying to charge you a minimum of thirty bucks to sell you an overthought software package to answer a five second question?

All I want to know is the mathematical formula used to figure out the number of rounds (not matches, but the number of rounds needed to schedule all the matches) in a double elimination tournament with X number of players... in this case 128. I'm not asking anyone to do the math for me. I'll do that myself, but I need to know the formula first.

I know one has to exist. People have been running these tournaments since long before there was computer software to design them. So, if you know what it is, I would be grateful if you would tell me.

Answer 1

For single elimination it's simple: log(2) N,

where N = # players.



So, for 128 players 7 rounds, which is

what the winner's bracket of double elimination will be too.



Now in double elimination, there is a loser's bracket alongside, starting with 1/2 the players (the ones

who lost in the first round).



Now the loser's bracket would also be 6 more rounds,

but we keep adding in more players as they drop out

of the winner's bracket.



Loser's bracket will go

Already there + Next round losers from WB = N -> N/2

(1) 0 + 64 = 64 -> 32

(2) 32 + 32 = 64 -> 32

(3) 32 + 16 = 48 -> 24

(4) 24 + 8 = 32 -> 16

(5) 16 + 4 = 20 -> 10

(6) 10 + 2 = 12 -> 6

(7) 6 + 1 = 7

(8,9,10) 7 + bye -> 4 -> 2 -> 1



So loser's bracket has 10 rounds,

and finally there is the final match of the tournament

between the winners of the two brackets.



7 rounds winner's bracket,

10 rounds loser's bracket,

Final match of tournament.



That's assuming there are no complications

like avoiding repeat matchups.

Answer 2

Double Elimination Formula

Answer 3

I think you have a misconception about what math is. Plugging numbers into a formula is not math. Figuring out the formula IS the math for this question. I'll give you two hints to this simple question.



(1) 128 = 2^7

(2) Try smaller cases, i.e. X = 2, 4, 8, etc.

Answer 4

Think!



2 players 1 round

4players 2 rounds

8 players 3 rounds

16 players 4 rounds

32 players 5 rounds

64 players 6 rounds

128 players your turn now to think!



see the pattern? the numbers on the left double-up

so for 4096 players you would need 12 rounds :)