Tric Trac Tournos
This format was developed by Mike Main (a k a MikeMadMonk), who runs tournaments in London (click here for details.
Typically a gathering of anything between six and twelve players would play each other in single games, scoring points as follows:
3 for a backgammon; 2 for a gammon; 1 for a single game; and 0.5 for a loss of any denomination.
When everybody has played everybody else, the points are totted up and the player with the most points is the winner.
The format is good for encouraging players to play deliberately for gammons, and is also great for social purposes in that you get to meet lots of players in a short space of time.