Gaming system and method providing a keno game including an additional number triggering event that causes at least one additional number to be added to a selected number set to form a modified number set

A method of operating a gaming system, said method comprising:

• (a) causing at least one processor to execute a plurality of instructions to operate with at least one display device to display a plurality of different numbers;
• (b) causing the at least one processor to execute the plurality of instructions to operate with at least one input device to receive, from a player, a selection of one or more of the plurality of different numbers and form a player number set including the one or more player-selected numbers;
• (c) causing the at least one processor to execute the plurality of instructions to randomly select a first quantity of the plurality of different numbers;
• (d) causing the at least one processor to execute the plurality of instructions to designate each number of the randomly selected first quantity of the plurality of different numbers as a designated number;
• (e) causing the at least one processor to execute the plurality of instructions to randomly select a second quantity of the plurality of different numbers and form a gaming system number set including the randomly selected second quantity of the plurality of different numbers;
• (f) if the gaming system number set includes at least one designated number:
• (i) for each designated number included in the gaming system number set:
• (A) causing the at least one processor to execute the plurality of instructions to causing the at least one processor to execute the plurality of instructions to randomly select a third quantity of the plurality of different numbers;
• and
• (B) add any number of the randomly selected third quantity of the plurality of different numbers that is not already included in the gaming system number set to the gaming system number set to form a modified gaming system number set;
• (ii) if the gaming system number set has been modified, causing the at least one processor to execute the plurality of instructions to determine any awards based on a comparison of the player number set with the modified gaming system number set;
• (iii) if the gaming system number set has not been modified, causing the at least one processor to execute the plurality of instructions to determine any awards based on a comparison of the player number set with the gaming system number set;
• and
• (iv) causing the at least one processor to execute the plurality of instructions to operate with the at least one display device to display any determined awards;
• and
• (g) if the gaming system number set does not include any designated numbers, causing the at least one processor to execute the plurality of instructions to determine any awards based on a comparison of the player number set with the gaming system number set and operate with the at least one display device to display any determined awards.

A non-transitory computer readable medium that stores a plurality of instructions which, when executed by at least one processor, cause the at least one processor to:

• (a) cause at least one display device to display a plurality of different numbers;
• (b) receive, from a player, a selection of one or more of the plurality of different numbers and form a player number set including the one or more player-selected numbers;
• (c) randomly select a first quantity of the plurality of different numbers;
• (d) designate each number of the randomly selected first quantity of the plurality of different numbers as a designated number;
• (e) randomly select a second quantity of the plurality of different numbers and form a gaming system number set including the randomly selected second quantity of the plurality of different numbers;
• (f) if the gaming system number set includes at least one designated number:
• (i) for each designated number included in the gaming system number set:
• (A) randomly select a third quantity of the plurality of different numbers;
• and
• (B) add any number of the randomly selected third quantity of the plurality of different numbers that is not already included in the gaming system number set to the gaming system number set to form a modified gaming system number set;
• (ii) if the gaming system number set has been modified, determine any awards based on a comparison of the player number set with the modified gaming system number set;
• (iii) if the gaming system number set has not been modified, determine any awards based on a comparison of the player number set with the gaming system number set;
• and
• (iv) cause the at least one display device to display any determined awards;
• and
• (g) if the gaming system number set does not include any designated numbers, determine any awards based on a comparison of the player number set with the gaming system number set and cause the at least one display device to display any determined awards.