A great three player game is “Cut Throat” where you rack a full rack of 15 balls then out of the three players one person breaks you can choose by any order you feel fell or a game of Rock, Paper, Scissors can be the chooser. After the ball break if no ball are sunk then the next person will shoot, if a ball is sunk then the first person will have the ability to choose which set of balls is his or hers. The three sets are 1-5, 6-10, 11-15 the object of the game is to sink everyone ball on the table and keep your balls on the table. So the the breaker sinks a 12 it is advantageous to choose one of the other sets preferably the one hardest to sink.
So example is if player 1 chooses the 6-10 ball and then runs the table out of all 1-5 and 11-15 then they are proclaimed the winner, but if player 1 misses the next shot and player 2 sinks a ball then chooses 11-15 the thier goal is to sink all of the other balls except 11-15.
If all of all the balls of a set get sunk in the middle of that game that player is eliminated and so forth until there is only one person standing.
There are shark rules involved such as you may shoot your own set of balls in to get to another shot or to no give up a turn, so if player 1 is still Set 6 -10 and there are only 2 choices to sink their own ball or lose the turn they may sink their own ball to get to another as long as they have enough balls on the table to keep playing.
If there is a scratch the next player in line get ball in hand and can place the cue ball anywhere on the table they choose.
This game is a more fun for three game and not very challenging at all for above average pool player but it is a great game if you have odd people at the table or just a three pack of friends with a possible 12 pack of booze.