A multileveled bonus round having a plurality of random generations, differing average awards and differing levels of risk. The gaming device contains a display that prompts the player to select one of a plurality of pick buttons. When the player does so, the game assigns an award set to each pick button of the display. The game then displays each of the awards in the award sets so that the player can easily recognize the assignments. The game randomly chooses one of the awards from each of the award sets and displays the chosen awards. The player's award for any given level is thus the selected award of the selected award set of the picked or chosen pick button. The awards of the present invention can be an award multiplier, outright base game credits or a bonus round terminator. A bonus round terminator terminates the bonus round. The game proceeds though all the levels of the round in the manner just described until the game selects a bonus round terminator or the player exhausts all the levels.