A gaming machine and a method of conducting a game of chance on the gaming machine are disclosed. The machine receives a wager from a player to purchase a series of plays of the game. In response to the wager, the machine provides the player with the series of plays and randomly generating at least one outcome for each play. The machine provides an accumulation feature that accumulates an element of the game over a plurality of the plays in the series and redeems the accumulated element for a bonus in response to a predetermined event in the game. The predetermined event may, for example, correspond to collection of a predetermined number of the element or a certain position of the element on a trail, feature ladder, or meter.