A gaming device having a game that includes several nearly missed outcomes associated with a designated outcome, where the player is provided an award for achieving a nearly missed outcome. If the player obtains the nearly missed outcome, the award is provided from a near miss insurance pool. Therefore, when a player nearly misses achieving a large jackpot, the gaming device provides the player with insurance payoff. In general, the near miss insurance pool is funded from a portion of each wager, and may be funded by several linked gaming devices.