The name Cutthroat--or as it's known on many college campuses, Screwyerbuddy--doesn't adequately convey the ruthless character required for the game. For starters, it demands three players; therefore, it is almost always played by two people who wanted to shoot pool and that omnipresently intrusive third party who always happens by, asking if perhaps he could join in this poolroom excursion. "I used to play a pretty mean game of bumper pool and..."
And with hostility hanging in the air, you resign yourself to playing Cutthroat, comforting yourself with the knowledge that this unwanted friendship will soon be on the rocks. A successful breaker gets to choose which balls will be his: numbers 1 through 5, 6 through 10, or 11 through 15. The next player to make a ball gets his choice of the remaining two groups, and the third player gets whichever group is left. Whoever has at least one ball from his group on the table when all the other balls are pocketed is the winner.
The object, in other words, is to pocket your opponent's balls. Thus, you'll want to snooker yourself in unsinkable positions as often as you can, all the while indiscriminately ridding the cloth of your cohorts'.
When not at the table, you will point out to the shooter the readily sinkable balls owned by the third player, just as you steer his sight from your own balls perched precariously on the lops of various pockets. This generally establishes a spirit of ill will that will last through the night. Make the loser pay for the beers.
Cutthroat is played under yet another name--Elimination. This name is particularly inapt, however, because when someone scratches, one of both of his opponents' balls is returned to the table. Thus, even though all of your balls may have fallen, you are not necessarily eliminated, and you'll find yourself coming back more often than a retired professional boxer.