Multiplayer Elimination Tournament - How does it generally work?

[DerIKM]

If T (total) players sign up, the number of players per game is between M (minimum) and P (preferred) and A (advance) players advance per game, how is the tournament structured?

I found tons of forum discussions about singular cases, but no general formula, which leaves me with a load of questions.
It would be easiest, if someone could send me the formula/algorithm/code... whatever, but I guess its not available. Therefore i guess I have to ask more singular questions.
I read that the algorithm involves free advances to handle odd numbers of (remaining) participants. The main purpose of my questions is to understand with which settings i can reduce the impact/amount of free advances.

1) Do always A players advance per game or will it sometimes deviate if this would allow avoiding free advances?

2) If M=P-1, will the first round always consist of rounded_up(T/P) games, namely (P+(-T mod P)) games with P-1 players and alle other game with P players?
That would seem intuitive, as it would avoid any free advances with the maximum possible number of P player games. However, the problem may be that the algorithm would have to deal with A*rounded_up(T/P) players after that, which may be a bad number to handle. E.g. if T=32, P=5, M=4, A=2 and they would set up 4 5p games and 3 4p games they would have to deal with 14 players in round 2 and 6 players in round 3, which is uncoverable with 4p and 5p games, so it has to give free advances. Does the algorithm plan ahead and create 8 4p games, so it can perfectly make 4/2/1 4p games in round 2/3/4? Or is it just gready in each round?

3) Id expect that i could reduce free advances by widening the range between M and P (more tolerance in game size) and by increasing A (more advancers->more rounds->more margin to fit the numbers). Do you agree?

[FSKFSK]

The way to do a Multiplayer Elimination tournament and not have things get weird is to do halves. When I make my 7 Wonders tournaments, I make it 2 players advance out of 3-4, or 3 players advance out of 4-6. This guarantees that you won't have any byes at all. (unless someone quits the tournament or someone is kicked for low reputation)

For example, if it's 2 of 3-4, at the end of the tournament you'll either have 6 people or 8 people left. If you have 8 people left, that's fine, two 4 person matches and a 4 person final. If you have 6 people left, that's fine, two 3 people matches in the semifinals and a 4 person final.

The tournament engine is not smart enough to make things even. If there's 49 tables in round one, it isn't smart enough to make 32 tables in round 2 and then everything is even after that.

A 4 of 5 elimination tournament just doesn't work. Suppose you have 10 people left. You have 2 matches of 5 and now you have 8 people left. Now 3 people get a bye to the final and there's a 5 person match with 2 advancing to the final. A 4 of 5 tournament is guaranteed to get weird at the end.

The way the tournament works is, if there aren't enough players to make 2 tables, it gives some people a bye to the final and then one game is played to fill the rest of the spots, even if that means more people get eliminated than how the tournament is configured.

The only way to make sure things don't get weird/unfair at the end is to do halves. 2 of 3-4, 3 of 4-6, 4 of 5-8, 5 of 6-10.

They really should overhaul tournaments, but BGA decided that implementing new games is a bigger priority than improving tournaments.

[DerIKM]

Thank you, that was helpful.

I wonder if i can make 2 advances out of 4-5p games work. If i understand correctly, the only way that it would become weird is, if it gets to a point where 6 players are left

[RazorOz]

Thank you, that was helpful.

I wonder if i can make 2 advances out of 4-5p games work. If i understand correctly, the only way that it would become weird is, if it gets to a point where 6 players are left

Use group stages and groups of 25 or 10, and you should be able to massage the numbers so you end up with 4 players. Just work backwards, so 4, 8, 16 etc., that would work into groups of 25 of 100 -> 40 -> 16 -> 8 -> 4. 200 would also work with group stages if you did 8 groups of 25, and 2 to qualify from each group, so you'd get 200 -> 80 -> 32 -> 16 -> 8 -> 4.

You can see an example of doing something like this here: https://boardgamearena.com/tournament?id=323651. I had it finish with 6 player tables, but you could do just the same thing finishing with 4 player tables.

The thing you need to remember is the system will always try to create table using the max number of players first, so in the example, it's impossible to have a table of 5 involved with 16 or 8 players left. In my example I used 25 player groups so the system couldn't possibly create 6 player tables to start etc. Whereas what you have to keep in mind is if you used a formula that left you 32 players after the group stage, the system would then created 4 5 player tables, and 3 4 player tables, which may lead to problems down the line, that's why in the second example I have made sure that when 32 players are left the tournament would still be in the group stage.

[DerIKM]

Use group stages and groups of 25 or 10, and you should be able to massage the numbers so you end up with 4 players. Just work backwards, so 4, 8, 16 etc., that would work into groups of 25 of 100 -> 40 -> 16 -> 8 -> 4. 200 would also work with group stages if you did 8 groups of 25, and 2 to qualify from each group, so you'd get 200 -> 80 -> 32 -> 16 -> 8 -> 4.

You can see an example of doing something like this here: https://boardgamearena.com/tournament?id=323651. I had it finish with 6 player tables, but you could do just the same thing finishing with 4 player tables.

The thing you need to remember is the system will always try to create table using the max number of players first, so in the example, it's impossible to have a table of 5 involved with 16 or 8 players left. In my example I used 25 player groups so the system couldn't possibly create 6 player tables to start etc. Whereas what you have to keep in mind is if you used a formula that left you 32 players after the group stage, the system would then created 4 5 player tables, and 3 4 player tables, which may lead to problems down the line, that's why in the second example I have made sure that when 32 players are left the tournament would still be in the group stage.

That's an awesome hint! I already found out that I can still change the tournament mode.
Currently there is 22 participants.
If the final number of participants is a problematic number between 26 and 35, it will create 6 or 7 games, resulting in 12 or 14 advancers, resulting in 3 games in round 2, resulting in 6 players advancing to round 3, where it would become problematic.
In this case I can use group stage in order to finetune the mode so that no byes will appear.
If the number of participants is 32 or more, I can make 8 groups, forcing it to make 8 4p games rather than 4 5p and 3 4p games, so i can then continue with 16 players. If the number is between 26 and 31 I would not be able to avoid that 6 or 7 games are created, but I could raise the number of advancers per group/game to 3, so i could continue with 18 or 21 which works fine

[DerIKM]

Unfortunately I cannot change the tournament mode after the first player has joined. So, I will have to hope that the participant count is a good number.
RazorOz, how do I make sure that the group stage settings are suitable, without knowing the participant count? Do I need to restrict the count to a certain range. It seems to me as if this range would have to be chosen quite narrow, since the groups themselves also must not have a bad number of players

[RazorOz]

Unfortunately I cannot change the tournament mode after the first player has joined. So, I will have to hope that the participant count is a good number.
RazorOz, how do I make sure that the group stage settings are suitable, without knowing the participant count? Do I need to restrict the count to a certain range. It seems to me as if this range would have to be chosen quite narrow, since the groups themselves also must not have a bad number of players

Easiest way is restrict it to a player count that will work. Normally I will have an idea of what I want beforehand, then make the tournament around that.

And yes, tournaments can be quite fragile this way, but tournaments can be fragile however you set them up. I get around it by hand recruiting the players for mine, but that will be more work than most are willing to put in, and helps if you are already involved in that game's community to know the player base etc.