A gaming device which provides a plurality of multi-component offers to a player and displays each offer to the player. Each multi-component offer includes a plurality of components having sub-components. The player can independently accept each component. Once a player accepts a component, the player receives a value based on the sub-components associated with that accepted component. The player continues to play the bonus game until the player has accepted all of the components in the offers or until there are no offers remaining. The gaming device then provides an award to the player based on the values of the accepted components of the offers.