In a system of linked gaming machines, upon a certain triggering event occurring, eligible gaming machines simultaneously receive a signal for initiating a free game bonus round. The players that have been playing the gaming machines will then play a certain number of free games in a competition with other players involved in the same bonus round. A free game pot, common to all the linked machines involved in the free games, pays all awards for the free games. Since the free game pot must fully support the free games prior to a free game round being initiated, and the requirement for the free game pot amount dynamically changes based on the number of eligible machines to be involved in the free game round, the percentage from the wagers for paid games allocated to the free game pot is dynamically adjusted.