The present invention provides a gaming device having a game that may be implemented in a primary or bonus game. More specifically, the present invention provides a processor controlled gaming device that presents a plurality of masked value choices to the player, provides a time period in which the player can elect to accept a masked choice and reveals and provides a value associated with the choice to the player if the player accepts in time. If the player does not accept in time or decides not to accept the choice, the gaming device, in one preferred embodiment, reveals the value the player could have accepted when the time period lapses or times out. When the player has successfully accepted a predefined number of masked choices, the game adds or multiplies the values yielded by the choices to form an award for the player.