Gaming machines or systems that provide for display of a current theoretical return-to-player (CTRTP) characteristic to the player during play of a game of chance are provided. Such gaming machines may also provide the player with opportunities (and notifications thereof) to increase the CTRTP characteristic by satisfying one or more CTRTP increase conditions associated with a credit wagering rate of the player on the gaming machine that the player is playing. Some such gaming machines may have automated wagering functionality in which the gaming machine may automatically place wagers for the player as long as certain conditions are met. In such gaming machines, the player may be able to control or influence the automatic wagering behavior of the gaming machine through the use of a rate selector that allows the player to change the wagering frequency and/or the wager amount used to place the automatic wagers.