A method of a house apportionment of a bonus value during bonus casino game play, entry for which occurs during play of an underlying game of chance. The method of house apportionment awards the player a portion of the bonus value for the bonus game and adds the remainder of the bonus value to at least one progressive account available to reward subsequent players, such that the bonus value paid by the house is constant and the house advantage is fixed regardless of player proficiency in the bonus casino game. The bonus casino games include knowledge-based playing. The knowledge-based bonus casino game includes a player answering, selecting, or guessing the proper responses to questions. The answering, selecting, or guessing has the step of challenging the player with questions having a common theme or varying difficulty. The knowledge-based playing has the step of asking the player questions the bonus value of which is measured against survey responses. Alternately, the amount of the bonus award may be based on time taken or clues received during the bonus casino game.