Ping wise, I agree also with @Raphael and @Emerald.
I would suggest letting similar pings play together first (as the flippers) and the ball be someone who has a much different ping. This might be fair for all players.
Also on how we decide the winners when it comes down to three players is the first round will decide on who the third place is going to be.
(Scenerio below)
Maybe we can add an incentive such as whoever volunteered/is picked as a ball received 1 additional ep when 2 rounds (your choice) has been played. If not, second scenerio is a staff member be the ball. But do choose appropriate player to be the ball for the two players.
We could also for example if the room size is an odd number, the one who's chosen to be the ball has to keep his or her position in the room. One way to kick/disqualify/slap the ball is if he or she stalls the game (does not press space) or other use other means to prolong the game.
In general this type of play is called juggling, so it might actually be fun and no I cannot try this by myself cause it's practically impossible.
But thanks given to the three trials.
Scenerio:
If player A vs B and player A wins, player B will play with player C.
If player C wins he or she will vs player A for first prize.
Player B will be considered third place.