The present disclosure provides a gaming device, a gaming system and a method for operating a gaming device or gaming system with a plurality of progressive awards. The gaming device enables a player to select one of the progressive awards. The player's selection of which progressive award to play for is based, at least in part, on a relative probability of the player winning the selected progressive award compared to the relative probabilities of the player winning the non-selected progressive awards. After selecting which award to play for, the gaming device either provides the selected progressive award to the player or modifies the relative probability that the player will win the selected progressive award with one or more of any award selections remaining. Such a configuration enables the player to strategically select which award to play for and the order that the player will play for the awards.