algorithm scheduling, round robin tournament with multi teams / game

Question

The round robin tournament algorithm works fine when only to teams meet per game. But how does one implement it for tournaments of sports or games where more then two teams meet in the same game. For instance a paintball tournament where 2 to n teams meet in 2 to n games. Still keeping the constraint that all teams should be home teams once and only once if possible (if the teams cannot be evenly divided then it is acceptable that as few teams as possible will not be home team)

Any ideas? The givens are number of teams, number of games. Possibly the number of team per game may be a given.

Answer 1

If you need 3 teams to play in the game you can use cubic represantation (so for n teams in the game it would be n-hypercube). That of course means that every possible pair of teams will play with every team - that's plenty of games. Total games played for each team is (n-1)(n-2)/2. Total games ever played is n*(n-1)(n-2)/3! (3 is number of teams per single game). So you can have (n-1)(n-2)/3! plays where every team plays as home. So, in general if we have k teams playing per single game, total plays per single team is (n-1)!/(n-k)!(k-1)!. Total games are n!/(n-k)!k!, and you can have (n-1)!/(n-k)!k! games played as home.