I wonder if 'shortest path' rather than 'longest path' is both more auditable and also encourages better tournaments. I feel like you could very easily design something complicated that exploits the longest path metric.

Sure. But just like the longest path calculation doesn't depend on the actual outcomes of the games, the shortest shouldn't either: best 2 out of 3 counts "2".

The interesting thing about X strikes as implemented by brackelope et al. is that the number of games doesn't vary very much--by only up to (X-1), as all players other than the winner have to lose X times.

However, the number of rounds this takes is a huge variable that depends on both luck and skill--if players fall out of the tournament early than the remaining players need to play more rounds to play the same number of games. This is averted significantly if the algorithm pairs players with the same number of losses each round insofar as possible (swiss pairings).

As an example of path difference, though, you can't go farther than the ladder-style tournament used in the PAPA circuit finals. If #1 seed wins, he's played 7 games. However, the lowest seeded players can play up to 16 more games before the final best-four-of-seven begins.

Josh, there are some crazy formats used here in Japan that I don't know how they'll grade out--have you been in touch with Horiguchi-san about the changes?

The first is for 'Pinball! Pinball! Pinball!': the event is timed. There is one match being played on each machine at all times. The loser of each game stays on the game, unless they lose two in a row in which case the winner stays on. The other player goes to the back of the not-currently-playing queue and awaits an opening to play more games, with the player winning the most games in three clock hours winning the tournament.

Second, there's a monthly 'high score tournament' that aggregates the high scores on six machines every month--I assume this is 12%, or does the very long qualifying time help?

Third, the 'normal tournaments' run here are as follows:
First, a qualifying round is played: each player plays each machine once.
Then players are divided into even and odd qualifiers and draft machine-positions: the first player can choose any player number on any machine, then the 2nd on any remaining machine, which is added to the other side of the bracket, and so on, with three machines on each side and all the odd-finishers in once side and the even finishers on the other. If there are fewer than 24 players, then a second machine-position is chosen starting from the last qualifier and working upwards, and then a third starting from first and working downwards. Thus, a given player might be playing in 1, 2, or 3 games depending on the draft.

All matches are played simultaneously, and the winners move on. Two machines on each side feed a quarterfinal, whose winner plays the last machine's winner in a semifinal. The two semifinal winners play for the title. As an amusing side-note each playoff round is played on the older of the two machines feeding that round.

If a player would play himself in a playoff round, he recieves a bye instead.

Japan has complicated tournaments.

Anyhow, could you grade those out for me

Yeah, it was super fun. Waiting in line to get to play again was even interesting, as you're hoping fast playing games that you're good at open up first.

That's probably about five games, then. It's a really odd format, but they run tournaments with it six times a year so they must like it...

Let me know if I can help with that somehow. I can act as an intermediary or whatever if that's helpful.

_{Post edited by Excalabur: Clicking fail}