Cut-throat racquetball allows three players to compete without a fourth. In this game, one player serves against the other two players, called returners. If the server wins the point, he continues to serve. If the two returners get a side out, then one of those two players becomes the server and the previous server becomes a returner.
The player who is the server competes against the other two players. The first player to get to 15 points wins. As the game starts, the server stands in the server's box and the returners divide the backcourt. One player stands on the right side and the other stands on the left side. The rules of this game are informal. On some courts, if the player on the right side of the court returns the serve, the player on the left side must return the next shot after the server hits it. Other clubs allow the receiving players to play at the front and back of the court and either can return any ball. As long as your group agrees on the rules, any consistent approach can work for cutthroat.
If the server hits a ball that cannot be returned to the front wall before it hits the floor, the server wins the point and serves again. If the returning team records a side out--no points are awarded to the defensive team in racquetball -- the player who started on the right side of the court becomes the server. The player who was on the left side moves to the right side and the server moves into the left return spot.
Although the two players who are returning the ball would seem to have a numerical advantage over their opponent, the server can take advantage of the rules of the game by hitting away from the player who is due to return the next ball. The returner who hit the previous shot may be in a perfect position to hit the next shot but he has to give up his position and let his partner hit it. The server may have the ability to put his opponents on the run if he can regularly hit the ball out of reach of the player who is due to hit the ball.