[gblake]

Originally Posted by Ether

There are 54 billion "useful" ways to pick the first match randomly for 6-team matches and 128 teams.

With each succeeding pick, the space of "useful" matches from which to randomly pick can be decreased using selection rules (e.g. don't assign teams to back-to-back matches; when any given team has been assigned 3 matches (for a 64-match tournament) drop them from the search space; etc)

I'm sure having a hard time conveying that I agree with you. You were right when you said "With just a bit of smarts, the number could be reduced greatly."

One useful method I like for the picking the initial match's alliances from among a field of N teams is using a user-defined seed to generate pseudorandom (integer) numbers between 1 and N until I have created a list of 6 unique numbers (4 for VRC or FTC, 2 for FLL?).

Another is to create a list of all m-team alliances (my past implementation ignored order (ignored which driver station a team would be assigned to in FRC)) and then iteratively use a user-defined seed to ... pick any two alliances that don't share any teams.

Neither of these requires dealing with 54 billion possible 6-team matches.

Originally Posted by Ether

I don't think it's mathematically guaranteed that you will achieve a valid tournament following this simple procedure. You may come to the last match and there's no valid match to pick from the remaining search space.

Don't forget this parenthetical statement from one of my earlier posts "(perhaps with some occasional backtracking)", and combine it with a "good enough" frame of mind.

Blake