1. A method of operating a gaming system, said method comprising: (a) causing at least one processor to execute a plurality of instructions to determine when an outcome enhancing condition is satisfied, (b) when the outcome enhancing condition is satisfied, enabling a player to elect to enhance at least one outcome, (c) enabling the player to select one of at least three different choices in association with a play of a game, wherein each of the choices either trumps or is trumped by at least one of the other choices, (d) causing the at least one processor to execute the plurality of instructions to select one of said choices, (e) when the outcome enhancing condition is not satisfied or the outcome enhancing condition is satisfied and the player elects not to enhance at least one outcome: (i) providing a draw outcome when the at least one processor's choice does not trump the player's choice and the player's choice does not trump the at least one processor's choice, and (ii) providing a lose outcome when the at least one processor's choice trumps the player's choice, and (f) when the outcome enhancing condition is satisfied and the player elects to enhance at least one outcome: (i) providing a win outcome when the at least one processor's choice does not trump the player's choice and the player's choice does not trump the at least one processor's choice, and (ii) providing the draw outcome when the at least one processor's choice trumps the player's choice.