Regarding match play, what you guys are talking about is the "Social Golfer Problem". There was an awesome link from Brown that now appears to be dead. This is the best I could find now.

http://www.mathpuzzle.com/MAA/54-Golf%20Tournaments/mathgames_08_14_07.html

There's some pretty complex math going on and it gets even more complicated if you want to make sure that no one plays the same game twice. I used the four groups of four solution from Brown to build the NGPL 2013 match play night @ my brothers and this years Cup. In both cases, I ran a simulation on my computer (overnight, for 3 nights) to do my best to balance the groupings.

The bottom line is, if you want to do match play with 20+ people while ensuring that no two players play each other and no one plays the same machine twice, you need a lot of rounds and a lot of games.

Given the right parameters, match play is a ton of fun. For larger numbers of players, most other formats work much better.