A gaming machine and a method of conducting a game of chance on the gaming machine are disclosed. In response to a wager from a player, the machine conducts a selection game including a plurality of selectable elements associated with respective outcomes. In response to a player's selection of one of the selectable elements, the machine awards the outcomes associated with the selected element and at least one of the non-selected elements. The awarded outcome may, for example, include a payoff, a bonus game, or awarding the outcome associated with yet another of the non-selected elements. If the awarded outcome includes the bonus game, the bonus game may re-trigger the selection game.