1. A method for playing a wagering game having a special payout, the method comprising: presenting a basic game having a plurality of randomly selected outcomes including a special-payout outcome; presenting a side-wager option for a player; in response to a player not choosing the side-wager option, providing the player with a first probability greater than zero of achieving the special-payout outcome; in response to the player choosing the side-wager option, providing the player with a second probability of achieving the special-payout outcome, the second probability being greater than the first probability; conducting the basic game with the first probability or the second probability, depending on the player's choice on the side-wager option; and in response to conducting, crediting the player the special payout when the special-payout outcome occurs in the basic game.