Abstract: A gaming machine has display means and a game control means arranged to control images displayed on the display means An underlying game is played in which one or more random events are caused to be displayed on the display means and, if a predefined winning event occurs, the machine awards a prize. On the occurrence of a predefined event, the player is offered a choice of two or more different prize sets. Each set containing a plurality of prize outcomes, from which prize sets a prize is to be drawn and awarded to the player, typically by a random process. The prize is drawn from the prize set or sets selected by the player from the two or more different prize sets. The sets of prizes may be presented on segments of wheels that can spin or simulate spinning before stopping randomly on a segment which defines the prize outcome won by the player.