Ring games or group games

Cowboy or Cowboy Pool is a fun game for 3or 4.
I copied the rules from Wikipedia (where the game is referred to as amateur).

Rulesedit

Conventional cowboy pool uses only four balls, the cue ball and three numbered balls, the one, three, and five.[6] The balls have a set opening placement: the one-ball is placed on the head spot; the three-ball on the foot spot; and the five-ball on the center spot. As in the game of snooker, balls that are pocketed are immediately respotted to their starting position. Beginning with ball in-hand from the kitchen – the area behind a pool table's head string – the incoming player must contact the three-ball first. If the player fails to do so, the opponent may either force the player to repeat the break shot, or elect to break themself.[7][9]

To win the match, a player needs to score 101 points. For the first 90, points are scored in three ways:

  • one point for performing a carom on the cue ball into any two object balls;
  • two points for caroming into all three object balls;
  • and the face value of any ball pocketed.
The maximum score possible on any single shot is 11 points, achieved by caroming off and pocketing all three balls. The failure to score in one of the delineated manners on any shot ends the player's inning at the table. All foulshots result in the player losing all points scored during the inning (not just those on the fouled stroke), and the opposing player comes to the table with the cue ball in position – except in the case of a scratch, which results in ball-in-hand from the kitchen.[7][9]

The 90th point in cowboy pool must be reached exactly, and the failure to do so is a foul resulting in a loss of turn.[9] For example, this means that a player with 89 points, who then scores 2 points rather than exactly 1, has committed a foul. Once the 90-point benchmark is reached, all points up to the 100th must be made by caroms. The pocketing of balls during this phase of the game gains no points.

The final point necessary to reach 101 and the win must be made by a losing hazard – an intentional scratch made by caroming the cue ball off of the one ball, scratching off either other ball is a foul
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A little clunky since you should write the scores as you go. But everyone keeps involved spotting balls and counting points.

If nothing else, it’s a good “palette cleanser “
 
Favorite game is Odd Ball and must go for the hit until the next shooter wants in. Cue ball scratch from behind the line. $.25 a way. Play 2 games. Pay up and rotate partners for 2 games. Good fun for a few hours. Nobody gets hurt.
8 odd balls
1 way for points (61)
Total 9… 5 ways win. No deductions.

3 people… cut throat.
8 or 9 ball. Captain .. rotate after game
 
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2 (scotch) vs 1, round robin works great for 3 players.
Flip for teams, then switch after each set.
After 3 sets, everyone has played with each of the other players, and by themselves.
 
Full rack pea pool
Everyone takes a pea, make your pea, everyone pays you, game over
If someone makes your pea you pay them. You keep shooting
Pull peas after every game to change order
 
I'm surprised that Bowlliards hasn't been mentioned.
It doesn't come to mind as a multiplayer game but there's no reason several couldn't play it in a group. That's true for all games where it is just player against the table. (The rules in the BCA rule book may be a little different from that site.)
 
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