Long story short: we want to make a tournament with exactly 13 players, with 13 rounds.
Let's assume we have 4 pins.
Each of the players will play 12 of the 13 rounds (in other words, skip one round).
During each round, four 3-player games are played, each on one of the four different pins.
For that tournament to be as fair as possible, I would like to find the way to organize rounds 1-13 so that:
- every participant plays against each of the 12 other players *exactly* twice (in total, you will face 12 x 2 players = 24 and you have 12 opponents)
- every participant plays 4 times as the first player, 4 times as the last player, 4 times as player #2
- every participant plays 3 games on Pin #1, 3 games on Pin #2, 3 games on Pin #3 and 3 games on Pin #4
$20 PP gift and my eternal thanks to the one who finds the solution to this problem (it's NOT trivial)
For example, round 1 may look like this (Player #13 does not play)... let me help filling the 12 remaining rounds!