The gaming system and method disclosed herein provides an award to one or more players for a non-occurrence of a designated event. The gaming system monitors a plurality of games played at a plurality of gaming devices. If the designated event occurs, the gaming system resets an event counter associated with tracking the non-occurrence of the designated event. If the designated event does not occur, the gaming system: (i) increments the event counter to account for the non-occurrence of the designated event, and (ii) determines if the quantity of games played since the last event occurred at least equals a predetermined quantity of games played. If the quantity of games played since the last event occurred at least equals the predetermined quantity, the gaming system provides one or more of the players an award for the non-occurrence of the designated event.