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 in association with a play of a game including at least different three choices, wherein each of the choices either trumps or is trumped by at least one of the other choices, and a win outcome a draw outcome and a lose outcome, wherein the win outcome is associated with a greater average expected payout than the draw outcome and the draw outcome is associated with a greater average expected payout than the lose outcome, (b) enabling a player to elect to enhance at least one outcome when the outcome enhancing condition is satisfied, (c) enabling the player to select one of said choices, (d) causing the at least one processor to execute the plurality of instructions to select one of said choices, (e) causing the at least one processor to execute the plurality of instructions to determine an outcome based on a comparison of the player's choice with the at least one processor's choice, (f) providing the win outcome when the player elected to enhance at least one outcome and the comparison of the player's choice with the at least one processor's choice results in a draw determination, and (g) providing the draw outcome when the player elected to enhance at least one outcome and the comparison of the player's choice with the at least one processor's choice results in a lose determination.