I was a member of something similar many years ago. It was called simply the men's club. Women were not allowed to be members. It was definitely more of a social club, but the basic model may work for a billiards club. There were tiers to the membership with the basic getting you a code to the front door.
Inside there were 4 or 5 poker tables, a 7 foot and 9 foot table, 3 electronic dart stations. There was a walk-in humidor, 5 or 6 flat screens, awesome bar, small dining room, and lounge area with leather sofas and easy chairs. The whole place had a state of the art filtration system.
The next membership tier got you a locker (mostly to store liquor) and the code to the walk in humidor.
The top tier got everything the others got along with a monthly box of cigars and maybe a different bottle of whiskey, can't remember.
It was available to members 24-7 except for Wednesday evenings when "mother" would come in and clean and restock the fridge with water and soft drinks.
Every other Friday night was a membership dinner provided by the club. guests were allowed, but it was pretty pricey. The club would have a couple of scantily clad girls to be servers and tend bar. They worked for tips only and probably made a killing.
The other two Fridays of the month were when you could bring wives or dates, but you had to pay for the dinner.
Mostly it was a bunch of rich older business men who sat around and smoked cigars and did questionable things with young girls out of sight of their wives.
I had the basic membership and I was paying $300 a month. I think the next tier was 500 and the highest was 1000 a month. When I left, we had 25 or 26 members and a waiting list half a mile long. Last I heard, they got some bad publicity for excluding women. They started letting the wives hangout and slowly people drifter away to other