I don't agree with getting a ping pong table for the open room - I think it would be better suited for the closed door room.
The noise that a ping pong table in the room will generate will most likely disturb residence of the units closest to the open room.
Who is going to ensure that residence and their visiting family/friends are not using this room at an unsuitable hour ?
Residence cannot even be respectful enough of the units nearest the mail room, elevator and the open room when coming in and out of the side door -a ping pong table will only increase the noise level.