If you’re really keen on maximizing the number of games for everyone, then you simply need to have more machines if you’re expecting that many people.
I would not do 3 strikes. I’ve seen a 3 strike tournament take 4+ hours with that number of players…at a location with 15+ machines.
If you have a few good players, 20 minutes is not enough time for 4 player games. They’ll go over on playing time alone, not to mention time wrangling between matches (and someone being in the bathroom, or at the bar, or outside smoking when it’s their turn).
And, the huge detriment for a knockout format is that you have to wait for a round to finish before you continue. So 20 people will have nothing to do while one group takes too long. With a double elim, you don’t have to wait for the entire round to finish.
Also with four player games, yeah, all four people are “playing”, but if you’re not in one of the first groups to play - it’ll be 30 minutes before you get to go. And if you have 16 people show up, then the first 12 will play…while four people wait, and then those 4 people will play while the other 12 people sit there waiting with two open machines.
Long story short: I vote for double elimination, 2 player matches. Have the game determined randomly, but maybe don’t let either player play a machine they played in the previous round.
Tough since this is your first tournament, but for me, I’ll brainstorm a few different formats ahead of time - and go with whatever makes sense for how many people actually show and the number of machines there are.
It’s easy to be optimistic that you’ll get 20, and then only have 10 show up. If it’s 10, maybe you do a 3 strike knockout tournament with 2 player matches. If it’s 12, that’s the perfect number for 4 player matches. If you have 16, maybe that’s a double elimination bracket.