A gaming device having a game which requires the same average investment from a player to win an award, including a jackpot award, regardless of the amount that the player bets at any one time. The award can be unchanging, e.g., $10,000, each time a player plays the gaming device. The award can also vary such as with a progressive jackpot, i.e., the jackpot builds until a player "hits" the jackpot. The game enables the average investment necessary to win the jackpot to be uniform by varying the odds of winning the jackpot as the player's bet varies. That is, a player betting less money needs to play the game more times, on average, to win the jackpot. Likewise, a player betting more money needs to play the game less times, on average, to win the jackpot. The average overall bet or investment thus remains constant despite the player's betting habits or betting ability.