Optimal table assignments for events.
I worked on these for the IGT, but I realised that posting them in the GT thread is probably going to get them lost, so I'm adding them here for people to find more easily in future.
These assume four players per table if possible, three if not. Underlined numbers are GMs.
9-12 Players on three tables:
Game 1: 1,6,7,12 - 2,4,5,8 - 3,9,10,11
Game 2: 1,4,7,9 - 2,3,6,11 - 5,8,10,12
Game 3: 1,3,6,8 - 2,4,9,10 - 5,7,11,12
Game 4: 1,2,5,11 - 3,4,7,10 - 6,8,9,12
If no player #11, put #3 in his place in game three.
If no player #10 either, put #4 in his place in game one, and #7 in his place in game two.
Randomise the GMing slots of any absent players.
Notes: Some attendees meet twice, but due to the GMing order, nobody plays together twice.
EDIT: As a natural consequence of people needing to meet twice, missing attendees may require some people to GM for the same players twice:
If #10 missing, #4 may GM for #7 twice.
If #11 missing, #2 may GM for #5 twice.
If #12 missing, #8 may GM for #6 twice.
There's no solution for this (four people from three tables means at least two have already met, players #1 to 9 have all GMed by the fourth round, so three people are meeting a previous GM in their final round) beyond trying to find other players in those games willing to volunteer or make sure #2, 4 or 8 are the players best prepared for GMing for the same player twice.
12-16 players on four tables:
Game 1: 1,5,9,13 - 2,6,10,14 - 3,7,11,15 - 4,8,12,16
Game 2: 1,7,10,16 - 2,8,9,15 - 3,5,12,14 - 4,6,11,13
Game 3: 1,8,11,14 - 2,7,12,13 - 3,6,9,16 - 4,5,10,15
Game 4: 1,6,12,15 - 2,5,11,16 - 3,8,10,13 - 4,7,9,14
If players #13-16 missing, all should be well, other than needing to randomise GMs in round 4.
Notes: No attendees meet twice.
Solutions for two or five tables will come at some point when I'm less busy. Six will come in the case we ever look like we're going to have more than 20 attendees at an event.