A cup tree
I would like the knockout tournaments to be shown in a cup three, that would make it easy for everyone to get an overview of the current and future rounds.

Twist to the current tournament formats
Knock out tournament with consolation games, that way everybody will get an equal or close to equal number of games, which would be nice when you play in a closed group of people (I know it is possible to set up by combining a lot of Knock out competitions, but it would be nice out of the box as a tick mark on the Knock out competition creation screen).
The possibility of odd number participants in round robin and knock out tournaments.
The possibility to decide on the number of participants in a tournament after creation. But off course before the first games are played. This way you don’t have to wait for the last couple of players that always forget to sign up or add AI opponents.

New tournaments
Double elimination (knock out)
You aren’t eliminated until you lose two games. If you lose a game you will play one of the other losers and the winner will play a loser from the next round of the original cup. In the final the one player how didn’t lose any games will play the one player who only lost once. If the player who already lost one game wins they will have to play one more game to decide the winner.