1. A gaming method for operating an electronic game on a gaming device, comprising: enabling a player to select one or more triggering events that trigger the updating of at least one game history counter, wherein the one or more triggering events are selected at a beginning of a game session associated with the gaming device; providing a dynamic paytable that describes a plurality of prizes that may be awarded during the game session, the dynamic paytable comprising, the at least one game history counter, and a threshold event that is engaged after one or more user selectable triggering events among the one or more triggering events occur, the threshold event configured to use the game history counter to determine if a particular user selectable triggering event results in a player award; displaying the game session on a display, wherein the game session includes a plurality of game events performed on the gamine device, each of the game events providing a player with an opportunity to be awarded one of the plurality of prizes; identifying with a meter one or more credits charged for each game event; modifying the dynamic paytable during the game session after one or more game events, wherein the dynamic paytable is configured to be calculated based on the probability of each threshold event occurring during each game event; modifying the dynamic paytable according to a graduated weighting function that weighs probabilities in the player's favor as more game events are played during the game session; and determining whether to continue the game session or to terminate said game session with a first button after each game event.