A gaming device that enables players to accumulate awards by activating an award
distributor having a plurality of award symbols and at least one selection group
activator symbol. The gaming device provides the player with a plurality of activations
where an award is associated with each award symbol indicated in each activation.
When a selection group activator symbol is indicated, the gaming device displays
at least one selection set having a plurality of selections associated with selection
awards. The gaming device enables a player to select one selection and provides
the associated selection award to the player. The number of available selections
in the selection set decreases by one after the player picks a selection. If the
selection group activator symbol is subsequently indicated, the player picks from
the remaining available selections in the selection set.