Game Play
When starting the game, the one-ball, six-ball, and eleven-ball should be placed on the three points of the rack. The one-ball is placed on the top where it is spotted.
In cutthroat, the "low" balls are 1-5, the "mid" balls are 6-10 and the "high" balls are 11-15. Each set of five balls is initially unclaimed, the assignment of groups of balls to each player is done during the initial stages of game play. The three players take turns attempting to knock any ball into a pocket. Once a player has knocked in a ball, he knows that he does not own that group of balls. For example, if a player started the game by hitting in the 3-ball and the 8-ball, he would own the high balls, as he has knocked in a low ball and mid ball. The other two players would still not have ownership over a set of balls, and would, during their turns, attempt to knock in balls to gain ownership over a set. This may vary by region. The most common variation is to assign the sets ahead of time in order of play (the first shooter is 1-5, the second shooter is 6-10, and the third shooter is 11-15).
A player's turn continues so long as he knocks in a ball with each shot. A shooter can even knock in his own ball, allowing him to continue a turn in exchange for the now-weakened position. This circumstance is called "cutting one's own throat." If a player sinks his own last ball, he must sit out the rest of the game unless another player scratches (see below).
Read more about this topic: Cutthroat (pool)
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