A game to be modified in accordance with the invention involves a first random outcome and a second random outcome that are combined according to game rules to produce a game outcome. The game is administered by receiving a player request for a specific entry, the specific entry replacing one of the random outcomes and being selected from a finite set of possibilities not determined by chance. The requested specific entry affects the probable outcome of the game. The specific entry is combined with the remaining one of the random outcomes according to the game rules to determine the game outcome. According to one embodiment, the specific entry may be a score such as 18 which replaces the player's hand in the game of blackjack.