Designing a Risk Tournament

[Hyacinthia]

I need help creating a schedule for a Risk Tournament.  I have some flexibility on determining the number of teams that will play.  We'd like it to be 8 or 10 or 12 teams.

Each game is set up with 4 opposing teams, meaning each team has 3 opponent teams in a game.   I'd like to get a balanced schedule.  I can create a balanced schedule for 16 teams, but we are just starting out, and can't get that many teams yet.   I have not been able to figure out how to get a balanced pattern for 8 or 10 or 12.  I could probably go with whatever number of teams would make it easiest to get a balanced schedule.

There will be several brackets that each team will compete in.  Ideally, I'd like each bracket to be balanced.  I hope I'm using the right term.  I mean each team should play each other team the same number of times, either once or twice or three times per bracket - or if necessary to get it to fit, the game could be balanced across two of the brackets : 4x5 +4x4 and 4x3+4x2
4x5 (4 teams; 5 members each team)
4x4
4x3
4x2
The number of players on the team does not affect the schedule.  But I'd like each team to be able to play each other team the same number of times.

Is this possible?  (Do I need to provide further information or clarification?)

[Ian Wakeling]

I am not sure that I understand about the brackets.  So more explanation may be necessary.

Does this solve the 8 team scenario with all teams competing against each other exactly 3 times?

For 12 teams follow the 'schedules' link near the top of this page, then enter 12 items and 'Whist'.  Treat each table of 4 players as a game involving 4 teams and this will give an 11 round schedule where all pairs of teams compete 3 times.

I feel there is something I have not understood.  Do you require the tournament to be played in rounds, like the two schedules I referred to above?  How do you see the 10 team tournament working?


  

[Hyacinthia]

Thank you very much for your prompt response.  

Because I'm new at this, I might be using the wrong terms.  I'll try to describe  what I mean.

I play team risk on line.  (That's why home and away don't really matter.  Everyone is home in cyberspace.  )

Each game has 4 opposing teams. (Each team in the game has 3 opponent teams.)   The size of the teams will vary from one game to another.  But within one game, each of the teams will start with the same number of team mates.   Games for teams using only 2 team mates will play on a smaller map, and have very different strategies, than games that have 5 team mates on each team.  

The number of teams in all games is the same (always 4 teams).  The size of the team determines the "bracket".  
The brackets we use are:
4x5 (4 teams consisting of 5 team mates each)
4x4 (4 teams consisting of 4 team mates each)
4x3 (4 teams consisting of 3 team mates each)
4x2 (4 teams consisting of 2 team mates each)
4x6 (we are considering trying out this size.  We might have one "flight?" for this size.  We will not attempt to balance that)


To win the tournament, a team should be able to win

- with in the most brackets
- against the largest number of different teams
- on many different map sizes

Each game takes 2 to 3 months to play.  Multiple games may be played simultaneously.  But too many games at once, or too long a run for the tournament, becomes burdensome.

The ideal format for the regular season would be to have 2 (or 3) games (for each team) in each of the 4 main brackets

2 - 4x5's
2 - 4x4's
2 - 4x3's
2 - 4x2's

and to have each team play all other opponents once.  

I realize this is not possible, because there would only be the opportunity to have 3 opponents in each game for a total of 6, when each team actually has 7 opponents.  We could bump it up to 3 games per bracket, but the game load would be larger than we want, making the tournament run too long.  Would this work better if we had just 7 teams in the league?  Or 10 (where 3 games should allow a team to play all 9 opponent teams?   But I suspect not all of the teams would play all of the other teams, then anyway.  These combinations seem to move around in odd ways when trying to get 4 teams to the table.)?


This is just the regular season.  Four teams will progress to a finals series.  It, too, will run a little over 3 months.

So we might have to make do with evening out the number of games each team plays against each other team by either spreading the balance over the entire 4 brackets, or balancing it over two groups.  

The 4x5's and 4x4's are both "large" games with the same maps, and similar strategies.  Same for the small games - the 4x3's and 4x2's.   The larger games depend a bit more on skill.  The smaller games are more strongly influenced by luck.   So one possibility would be to balance over the whole regular season series by doing
 
2 - 4x5's
2 - 4x4's
1 - 4x3
1 - 4x2
and adding in
1 - 4x6
to make up the 7 rounds described in the message you linked to me.

It's most important for the large games to be more balanced.  At the bare minimum, each team should play every other team at least once.  Better would be to get those 4 rounds as balanced as possible.

We don't know how many teams will sign up for this new league.   Because we want to launch soon, we might only get 8 teams.  But we're willing to accept up to 12.  

I don't know how to determine which would be easiest to get closest to the ideal of balanced.  But if one of them (8 or 10 or 12) is easier to balance we'd promote for that.

I hope this gives a clearer picture.  Again, thank you very much for your help.  

[Hyacinthia]

Figured out how to use the whist tables.  But what I don't quite understand, for 16 players the whist table uses 15 rounds.  It's possible to get all 16 balanced over 5 rounds in the kind of set up I need.  15 is waaay overkill.   I mean, I do understand, because it's for whist, and you have partners in whist, pairs of pairs, not 4 opponents facing each other.  So it's not quite the same.  I just wonder if I could similarly get 8 into balance with less than 7 rounds.

[Ian Wakeling]

This looks to be a complex problem and I think you will need to use some form of computer optimization to come up with a practical solution.  I am still confused as to the overall objective. Perhaps you should be thinking it terms of the individual players rather than 8, 10, or 12 teams.  Surely if the size of the team is variable, an individual is going to be on different teams with different team-mates/partners during the course of your tournament.  So is partner balance just as important as the opponent balance?

I am not sure how you are going to make use of them, but I can help with other schedules similar to the two that I showed above.  8 can't be made to balance with less than 7 rounds as the number of possible opponents that one team has (i.e. 7 opponents) is not divisible by 3.  With 16, there are 15 possible opponents and it turns out that it is possible to arrange that each team has 5 games, with 3 different opponents each time,  so 15 = 5 x 3 , but there are relatively few scenarios where the numbers work out like this.