A gaming apparatus, such as a slot machine, that randomly determines a combination of symbols and pays prizes according to a determined payout table, is used to perform a gaming method similar to conventional slot machine play, but that permits greater interaction with the player. The gaming method provides the player with the option of increasing an amount wagered after at least one of the symbols has been determined. The method additionally provides the player with the option to randomly determine a symbol or symbols a second time, or to force a symbol to be the same as a symbol already determined, optionally at additional cost. The method includes making appropriate adjustments to a payout table, depending on the player's actions during game play.