In one embodiment, a gaming machine carries out a main game, such as a spinning reel type game, either using physical reels or simulated reels on a video screen. A special combination of symbols activates a video bonus game. The bonus game comprises a matrix of hidden values in the form of icons that may be selected by the player. The values that may be selected are displayed to the player in an order unrelated to the arrangement of the hidden values in the matrix so the player sees what she can possibly win. The player then makes her selections to win the hidden awards. In one embodiment, the player only makes a predetermined number of selections. In another embodiment, the player makes selections until an end-of-game value is selected. After each selection, the displayed values may change.