Gaming system and method for increasing the likelihood of obtaining a designated outcome for a play of a game

A gaming system comprising:

• a housing comprising an access door;
• a security monitoring circuit supported by the housing and configured to monitor the access door;
• a power distribution component supported by the housing;
• a plurality of output devices comprising a display device supported by the housing, a player tracking display supported by the housing, and a speaker supported by the housing;
• a sound card supported by the housing and operable with the speaker;
• a processor;
• a plurality of input devices comprising a touch screen input device supported by the housing and operable with the display device, a wagering input device supported by the housing, and a cashout input device supported by the housing;
• an acceptor configured to receive a physical item associated with a monetary value;
• and
• a memory device that stores instructions that, when executed by the processor, cause the processor to:
• establish a credit balance responsive to receipt, by the acceptor, of the physical item;
• place a wager on a first play of the game responsive to receipt of a wager input by the wagering input device and cause the credit balance to decrease based on the wager;
• for the first play of a game, randomly select an initial hand of cards from a first deck of cards comprising a predetermined first quantity of a plurality of cards;
• cause a display of the initial hand of cards by a display device;
• for each card of the initial hand of cards, designate that card as either a held card or a discarded card responsive to receipt of an input by the input device;
• responsive to determining that all of the cards of the initial hand of cards are held cards, designate the initial hand of cards as a final hand of cards;
• responsive to determining that one or more of the cards of the initial hand of cards are discarded cards, form the final hand of cards by, for each discarded card of the initial hand of cards, randomly selecting a replacement card from the first deck of cards and replacing that discarded card with that randomly selected replacement card;
• cause a display of the final hand of cards by the display device;
• determine any award, based at least in part on the wager, associated with the final hand of cards;
• cause a display of any award associated with the final hand of cards by the display device;
• cause the credit balance to increase based on any award associated with the final hand of cards;
• responsive to an occurrence of a triggering event in association with the first play of the game, award a free play of the game and use a second deck of cards comprising a predetermined second quantity of a plurality of cards for the free play of the game, the triggering event causes a modification of the second deck of cards to include more cards in the second quantity of cards of the second deck of cards than the first quantity of cards of the first deck of cards such that a probability of obtaining a designated final hand of cards via the modified second deck of cards in the free play of the game is greater than a probability of obtaining the designated final hand via the first hand of cards in the first play;
• and
• initiate a payout responsive to receipt of a cashout input by the cashout input device.