Abstract: An apparatus and a method facilitate single user and tournament play of wagering games on a computer-controlled machine. A player provides control input in order to control the game. The machine simulates the rolling of dice to obtain scoring combinations, and the player makes strategic gaming decisions concerning the holding, releasing and re-rolling of the dice, and the assignment of the resulting dice combinations to scoring categories. A game progresses as a player attempts to fill a plurality of scoring categories in order to achieve a high total score. A player wagers on each simulated roll of the dice, and is paid for winning assignments of combinations to categories. The computer-controlled slot machines are generally linked to a wide area network, facilitating tournament play among multiple players and progressive jackpots. Computer-controlled slot machines include machine-readable media reading and writing devices, allowing players to save and restore games in progress.