A central determination gaming system with a keno game. Upon a player initiating a game play at gaming terminal, the gaming terminal enables the player to select a plurality of symbols. The gaming terminal accesses a standard set of predefined symbols for the specific game played. The gaming terminal bidirectionally maps the player's selected symbols with the standard set of predefined symbols. The gaming terminal receives a predetermined game outcome seed from a central controller. The gaming terminal utilizes the selected game outcome seed to generate a plurality of game symbols. The gaming terminal determines if each of the generated game symbols needs to be modified. If so, the gaming terminal modifies these generated game symbols based on the bidirectionally mapping, presents the modified game symbols to the player and provides the player a game outcome that is determined based on the selected game outcome seed.