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 being selected independently of player selection, the randomly selected outcomes including a special-payout outcome; accepting a basic wager from a player for the basic game between a minimum and maximum amount via a wager input device; presenting an additional, separate side-wager option for a player to place an additional side-wager via the wager input device, the side wager distinct from the accepted basic wager, the side-wager option requiring a side-wager amount in addition to the accepted basic wager; in response to a player not choosing the side-wager option, one or more processors 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, the one or more processors providing the player with a second probability of achieving the special-payout outcome, the second probability being greater than the first probability; via the one or more processors, conducting the basic game with the first probability if the player does not choose the side-wager option, or the second probability if the player chooses 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.