Systems and methods for use with a gaming machine that, in response to the staking of a wager by a player, is arranged to randomly determine an outcome of a game, display on a display representations of the outcome, and award an award if a winning outcome occurs, wherein the player can stake a variable sized wager on the occurrence of a winning outcome, the systems and methods including varying the probability of selecting the outcome associated with a special prize dependent on the size of the wager staked by the player and/or varying the probability of one or more other prizes that are alternatives to the special prize.