A gaming system and associated methodology include means for a player to place a wager to participate in play of a plurality of base games, the wager entitling the player to a block of credits. A central lottery computer system is configured to randomly divide the block of credits between the plurality of base games and to conduct the plurality of base games. Means are provided for the player to interact with the central lottery computer system for simulated play of each of the plurality of base games. A prize is awarded for a winning play of any one of the base games and is a function of the number of credits that were randomly assigned to the respective base game by the central lottery computer system.