9 players in groups of 4

[cjpalermo]

So - I'm in the process of setting up a schedule for some online games for my tabletop board gaming group.

The two player stuff is easy - there are websites dedicated to that.

Setting up three player games, where each player plays with each other player once is easy (because I found a site where someone had the same inquiry; and I grabbed the answer).

But, the online game plays 2, 3 or 4 players - so there is interest in scheduling 4-player games.

What would be the way to schedule a group of 9 players into 4-player games so that each player plays in a game with each other player *at least* once (I suspect there will be some double-ups, since 8 (the remaining number of players besides *me*) doesn't divide into 3 (the number of players needed at each table besides *me*).

And, since I suspect this will come up each month - where the game changes, and maybe there'll be 7 players in tables of 5; or 11 players in tables of 3  - how would I tackle this formulaicly?

Thanks!

[Ian Wakeling]

There is no simple formula for making the schedules that you want, instead you would need to create an algorithm that optimizes the schedule to your requirements (by searching a lot of different ones).  If you can play enough games, then for some numbers of players there are balanced solutions for 4-player games.  The 9 players and 2 games is one such example, as you can take the Whist schedule for 9 players, and ignoring the 2 vs 2 aspect, consider the schedule to be simple 4 player games, then every player would play with all others exactly 3 times over the 9 rounds.  Other Whist schedules that you can find on the Wiseman site and here by following the "inspired the forum" link at the top of this page may also be useful.

Two questions. Are you wanting to play games simultaneously in rounds (so in each round two 4-player games happen at the same time)?  Are you willing to play more games to achieve a balanced schedule, or are you really looking for the minimum number of games so that all pairs play together at least once?