Gaming system and method providing a multiplay game with resultant symbols

A gaming system comprising:

• a first gaming device comprising:
• (a) a first housing;
• (b) a first at least one processor;
• (c) a first at least one display device supported by the first housing;
• (d) a first plurality of input devices supported by the first housing and including a first acceptor;
• and
• (e) a first at least one memory device that stores a first plurality of instructions that, when executed by the first at least one processor, cause the first at least one processor to operate with the first at least one display device and the first plurality of input devices to:
• (1) if a first physical item associated with a first monetary value is received by the first acceptor, establish a credit balance for a first player based at least in part on the first monetary value;
• and
• (2) following receipt of a first wager deductable from the credit balance of the first player, for a first play of a first game, randomly generate and display a first plurality of symbols of a first set of a plurality of symbols at a first plurality of symbol display areas, the first set of symbols including a first designated symbol;
• a second gaming device comprising:
• (a) a second housing;
• (b) a second at least one processor;
• (c) a second at least one display device supported by the second housing;
• (d) a second plurality of input devices supported by the second housing and including a second acceptor;
• and
• (e) a second at least one memory device that stores a second plurality of instructions that, when executed by the second at least one processor, cause the second at least one processor to operate with the second at least one display device and the second plurality of input devices to:
• (1) if a second physical item associated with a second monetary value is received by the second acceptor, establish a credit balance for a second player based at least in part on the second monetary value;
• and
• (2) following receipt of a second wager deductable from the credit balance of the second player, for a first play of a second game, randomly generate and display a second plurality of symbols of a second set of a plurality of symbols at a second plurality of symbol display areas, the second set of symbols including a second designated symbol that has a designated relationship with the first designated symbol;
• and
• a server including at least one server processor and at least one server memory device that stores a plurality of server instructions that, when executed by the at least one server processor, cause the at least one server processor to operate with the first and second gaming devices to, if the displayed first plurality of symbols includes the first designated symbol and the displayed second plurality of symbols includes the second designated symbol:
• (a) form a resultant symbol from the first and second designated symbols,
• (b) accumulate said formed resultant symbol, and
• (c) if a designated quantity of formed resultant symbols has been accumulated, cause a first award to be provided to the first player and a second award to be provided to the second player.