Hello, I've been fascinated with tournament systems and am a bit stuck on this seemingly simple question. For a round-robin tournament consisting of 1v1 matchups of *n* contestants, you have *(n / 2) \* (n - 1)* rounds. E.g. a round-robin tournament of 16 would need 8 \* 15 = 120 total matches to complete.
I'm stuck on how the number of total matches changes if you increase a match size to *m* contestants per match. My application of a Mario kart tournament usually involves matches of 4, but I'm curious if there's a model for an arbitrary size *m* where *m <= n*.
The criteria for a round-robin tournament of match-size *m* would require each contestant to play every other contestant *at least once*. For example, a tournament consisting of a match-size of 4 with 8 total contestants, *a, b, c, d, e ,f, g, h,* would consist of the following matchups.
Which yields 6 total matches, in this case. I've done some googling and haven't found a good answer for a general equation. Would anyone happen to know, or be able to point me to the right resource? Thank you! (giving this a discrete math flair because I don't see a combinatorics flair, apologies if that's incorrect!)