A central determination gaming system which provides a player a choice in outcomes. In one embodiment of the present invention, upon a player initiating a game play at one of a plurality of gaming terminals in communication with a central controller, the central controller selects a plurality of game outcomes from a pool of game outcomes. The selected game outcomes are communicated to the gaming terminal and the gaming terminal provides one of the selected game outcomes to the player based on at least one choice made by the player regarding the game play. The provided game outcome is prevented from further selections from the pool of game outcomes.