I have to arrange a small tournament (bowls if you're interested). There are 12 entrants and each player has to play 5 games, each against a different opponent. That wasn't difficult to arrange using random selection. But if there had been an odd number of entrants, would it be possible for them each to play an odd number of games? I can't see that it would. I think it would have to be an even number of games. Am I right?
Have you looked at Berger Pairings charts? They might be of some help.
Google it and you should be able to find details and sample charts.
Their charts cover odd and even group sizes.
The individual round match-ups are listed out for the full even number group size, but if the actual group size is one less, then in each round one player sits out for that round when matched up against the 'blank' player. (hope that makes sense)
You specified that each player was to play 5 games. Was that a total games limit or just a minimum limit for each player?
If you did 'round robins', you could divide your 12 players into 3 groups of 4 players, but then each player would end up playing 6 games each, but only against the 3 other players within their group. (2 games against each, one as black and one as white)
Another round robin option would be to have two groups of six, and each player would play just a single game against every other player in their group. You would need to try and balance out the games for playing black or white, but you would get your 5 games that way. Hopefully each player would end up with 3 playing one color and 2 as the other.
Hoping this may have helped in some way. 🙂