- Players: 4
- Game type: Billiards, cutthroat
- Objective: Eliminate all other sets of balls except your own.
The players first determine order of turns, which remains fixed during the game. The winner of the previous game, if any, begins first.
The balls are divided into four sets. This may seem unusual, given that there only 15 balls, except the white cue ball is designated as ball 16. (Hereafter, the term cue ball does not necessarily refer to ball 16.) The sets are: set A (1-4), set B (5-8), set C (9-12), and set D (13-16). Each player is eventually assigned a set of balls, in which case that player and set are called determinate. Otherwise, a player is considered indeterminate; all players begin the game in an indeterminate state.
To determine what set is assigned to what player, each player records the set of the balls he/she has sunk. A player cannot be assigned to a set he/she has sunk. As the game progresses, the players can logically deduce their determinancy from process of elimination. Determinancy is re-evaluated after each shot.
For indeterminate players, the cue ball (not necessarily ball 16) is the highest remaining ball of a particular indeterminate set known as the cue set. At the start of the game, the cue set is set D and the cue set rotates downward through the remaining indeterminate sets. So, the cue is ball 16 of set D at the beginning of the game; the next player uses ball 12 (or next highest ball) of set C (provided that the set remains and set C is not determinate). For determinate players, the cue ball is the highest remaining ball of their set. Note that a player may have to change cue balls in the same turn if determinancy is decided during that turn.
If determinate, a player receives a turn provided that at least one ball of his/her set remains on the table. If indeterminate, a player receives a turn provided that at least one indeterminate ball remains on the table. A player continues their turn provided that at least one ball is sunk, regardless of whose ball it is, and the above still holds. If the player scratches, the cue and the highest ball of all other determinate players is placed on the table (placed on the midline). The next player then goes.
If only one player's balls remain, that player wins.
Sudden Death Rule: If all players agree, the rule of replacing balls on scratches (including the scratched ball) can be suspended to expedite the game.
Quac stands for Queen Anne's Cutthroat, which was invented as a variant of cutthroat that allowed for an extra player. Some say the game really is quacked. It was created by the Queen Anne's crew on or about September 1999.