A system and method for operating a game of chance. A gaming system includes one or more game displays, a user interface, at least one processor running executable instructions related to a game of chance and memory in communication with said at least one processor. The game of chance including a two-part game wherein at least one part of the two-part games includes a video reel game and includes the generation of random sub-events wherein two or more of said random sub-events are required to trigger another game part including a bonus game, a secondary game, a free game round, a “hold and spin” round, or other game event. The plurality of sub-events required to trigger another game part serve to reduce the frequency of significant player “cold streaks” during game play. The game of chance including a plurality of user-selectable or switchable random number generators in communication with the at least one processor.