A gaming system which employs one or more random determinations to redistribute award amounts or value not captured by lower-skilled players to higher-skilled players. The gaming system funds a skill award pool based on one or more awards that lower-skilled players (or no-skill players) failed to win in association with one or more skill-based games. The gaming system utilizes the escrowed amounts in the skill award pool to provide one or more supplemental awards to higher-skilled players, wherein the qualification to be provided a supplemental award and/or the amount of the randomly determined supplemental award are based, at least in part, on the one or more skill-based inputs made in association with the play of the skill-based game.