The present invention provides a bonus round of gaming device in which the player either wins that which the player does not select or the player selectively replaces one award with another award with the hopes of maximizing an ultimate award. In the embodiment wherein the player wins that which the player does not select, one or more selections are made from the plurality of symbols, and the game provides awards assigned to the unselected choices or symbols. In the replacement embodiment, the game replaces the award of a selected symbol with an alternative type of award. In one example, the awards assigned to the unselected symbols are gaming device credits, while the converted or replaced awards assigned to selected symbols are multipliers. After replacement, the game sums the credits, sums the multipliers and multiplies the credits by the multipliers to produce an ultimate award.