Gaming system and method providing a bonus opportunity when a designated relationship exists between a plurality of randomly determined elements

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

• generating, by a processor of the gaming system server, a primary game outcome in association with a play of a primary game;
• communicating first data that results in a display device that is remote from the gaming system server displaying the primary game outcome;
• determining, by the processor, whether the primary game outcome is a winning outcome or a losing outcome;
• separate from the generation of the primary game outcome and before the display device displays the generated primary game outcome, randomly determining, by the processor, two or more of a plurality of elements, each element associated with one of multiple different characteristics, in association with a play of a secondary game and communicating second data that results in the display device displaying the two or more randomly-determined elements;
• before the display device displays the generated primary game outcome, determining, by the processor, whether a designated relationship exists between the two or more randomly determined elements, wherein the designated relationship exists if the two or more randomly determined elements are each associated with a same one of the characteristics;
• responsive to determining that the designated relationship does not exist between the two or more randomly determined elements and that the primary game outcome is the winning outcome, determining, by the processor, a primary game award based on the primary game outcome and communicating third data that results in the display device displaying the primary game award;
• responsive to determining that the designated relationship exists between the two or more randomly determined elements and that the primary game outcome is the winning outcome, determining, by the processor, a modifier and determining, by the processor, the primary game award based on the primary game outcome and the modifier and communicating fourth data that results in the display device displaying the primary game award;
• and
• responsive to determining that the designated relationship exists between the two or more randomly determined elements and that the primary game outcome is the losing outcome, not determining, by the processor, any primary game award based on the existence of the designated relationship.