A gaming system comprising a regulated gaming machine primarily dedicated to playing at least one casino wagering game. The gaming machine includes an electronic display device and one or more electronic input devices and game-logic circuitry configured to detect and accept a physical item associated with a monetary value that establishes a credit balance. The game-logic circuitry initiates the casino wagering game in response to an input indicative of a wager covered by the credit balance, increments one or more progressive jackpots associated with the wagering game, conducts a skill-based bonus game that awards portions of the incremented progressive jackpot based on skillful inputs of a player and receives a cashout input that initiates a payout from the credit balance. The game-logic circuitry is further configured to alter one or more aspects of the skill-based bonus game to maintain the average return to player (RTP) within an acceptable range.