[Gabe]

For this amount of trouble, lets step away from algorithms and any other sort of computerized system, as any kind of solution is bound to result in patterns, which we want to avoid to have a fair game.

This is my solution, and a very simple one. For each regional FIRST should buy popsicle sticks for as many teams as are attending. If there are 48 teams for the SV regional, FIRST buys 48 popsicle sticks. Each stick will have one team number written on it. Then they are all placed into a corrugated cardboard box with a lid. You shake the box really hard for five seconds, and then open it. Without looking, a person picks out sticks three at a time, forming alliances. After all of the sticks have been picked and having recorded the alliances, all 48 sticks are placed back in the box and the process is repeated as many times as necessary.

For added effect I suggest that the choosing of alliances be done in plain view of all of the teams. This will generate a lot of excitement as well as doing away with any doubt of having truly "random" match schedules.

(I think this is a realistic and fair way of chosing alliances.)