Various embodiments of the gaming system of the present disclosure enable a player to play a secondary or bonus game, in which the player has the chance to play for a designated award in the triggered secondary or bonus game. The probability of triggering the secondary or bonus game varies based on the player's primary game wager. Additionally, the probability of winning a designated award in the triggered secondary or bonus game varies based on the player's primary game wager. In one embodiment, as the primary game wager increases, the odds of triggering the secondary or bonus game increase, but not in direct proportion to the wager. Similarly, the odds of winning the designated award in the triggered secondary or bonus game increases, but not in direct proportion to the wager.