[TomCollins]

I probably explained this poorly.

Suppose I have a team game that takes 3 players at a time. I want to schedule a series of games that has each player be in a game with every other player at least once, but no more than twice.

For example:
Game 1 Game 2
ABC DEF
ADE BCF
ABF CDE

In this case, a plays everyone once, and B twice. But D plays E 3 times, and doesn't play B ever.

There has to be some math-y name for this type of thing.

For 6 players in 3-man games, I think you'd have to have 4 matches. But I'm not even sure I can satisfy the play once but not twice criteria.