@umhia
I don't know about balancing system.
If you check the last tournament lichess.org/tournament/lGyNRRcW , you see that, for example, Fumitoks (3rd) played 3 times with TheOneTrapMan (4th) in the end - probably in the end they were always close, so the system paired them when possible (this possibility is an advantage of arenas over the Swiss system).
And in general, in the arena, how many games you play with one opponent depends on the duration of the tournament and the number of participants. The lower the number of participants and the longer the duration, the more likely you are to play some opponents more than 1/2/3/... times.
I don't know about balancing system.
If you check the last tournament lichess.org/tournament/lGyNRRcW , you see that, for example, Fumitoks (3rd) played 3 times with TheOneTrapMan (4th) in the end - probably in the end they were always close, so the system paired them when possible (this possibility is an advantage of arenas over the Swiss system).
And in general, in the arena, how many games you play with one opponent depends on the duration of the tournament and the number of participants. The lower the number of participants and the longer the duration, the more likely you are to play some opponents more than 1/2/3/... times.