Cutthroat is a three-player pocket billiards game, played on a pool table using cue sticks. Each player is assigned a set of numbered balls. The object is to be the last player with at least one ball still on the table. Subtle differences in game rules exist, with numerous regional variants.(see Regional Variations of Cutthroat) The name "cutthroat" is not unique to pool, but refers to any game played with three or more players in which each player must fend for himself (such as cutthroat bridge).
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).
Another peculiarity of this game is the consequence of scratch, or knocking the cue ball into a pocket. In most circumstances, a player's opponents are "rewarded" by taking one of their balls each out of the pockets, and spotting them back onto the table. If (on the same turn) a scratch occurs after first pocketing an opponent's ball, it remains that only one ball per opponent may be returned to the table. The purpose is not to nullify the effects of the scratch, but to punish the offender and reward the other players. Therefore, any ball pocketed prior to the scratch (on the same turn) remains in the pockets; otherwise the potentially unaffected third player could be placed at a disadvantage [through no fault of his own]. After the scratch, any of the opponent's balls can be selected to be placed back on the table. In some regional variants, and in particular, when played in bars with coin-operated tables where balls cannot be removed at will, true "fairness," is an impossibility. Additional unbiased rules prove essential to maintaining a fair game. In this circumstance, the player who scratches selects one of his or her own balls to be pocketed immediately. No balls are to be returned to the table. Other variants allow the next player ball-in-hand. Again, in the event that a scratch first pockets an opponent's ball in a coin operated game, no remaining balls may be substituted/ traded, however, the affected player is permitted to select the ball [belonging to the offender] which is to be removed. This not only nullifies the offense, but helps to ensure that no two players can secretly team up to eliminate another. In the extreme peculiarity that the final shot leaves only the cue ball on the table (i.e. a player has pocketed his opponent's ball and inadvertently his own ball in a single shot) 1 ball of each set will be placed at the break mark and the shooting player continues. If a player places one of their own balls into a pocket it is considered a scratch and the next player plays. However after a player knocks in their own ball, no balls are returned to the table.
Winning the game
The object is to be the last player with at least one ball left on the table. When a player has no balls on the table, he is said to be 'out' and his shot is skipped in the rotation of taking shots. Under normal rules (where balls are retrieved on a scratch), if one of the remaining players scratches, the "out" man can recover a ball and return to the game.
Various point systems may be used to play matches or sets, rather than just one game. With its uniqueness as a three player game, counting games won is possible but does not give credit for finishing second. One system is awarding three points for a win, plus an additional one point for each of the winner's remaining balls at the end of each game. The player last eliminated receives two points, the first eliminated player none. There may also be a bonus awarded for playing a perfect game, sinking both opponents' sets of 5 balls while having all 5 of yours remaining (Usually 2 points, making a perfect game worth 10 points total: 3 for the win, 5 for remaining balls, plus 2 bonus). This system adds great importance and strategy regarding whom to eliminate first as the match goes on, often creating alliances of the two trailing players to catch the leader in points. The match may be won by reaching a set amount of points, or reaching a set deadline in time.
The game is also potentially playable by five players, each player owning three balls, rather than five.