In some embodiments, a player may influence the volatility of a bonus round of a game by placing elements collected during a primary game onto symbol positions of the bonus round. In some embodiments, if a symbol position onto which a player placed one or more bonus round symbols is selected as an active symbol position for an event instance of the bonus round, the player wins a prize. Additionally, a multiplier may be applied to the value of the prize or other benefit may be provided to the player if the player placed more than one bonus round symbol element on the position. Thus, a player having a plurality of bonus round symbols to place may choose to increase the frequency of prizes won (e.g., by distributing the bonus round symbols over more positions) or increase the value of prizes (e.g., by grouping more symbols on fewer positions).