Presented is a system and method for generating bingo game bonuses that are non-banked, for use with pooled bingo games. The system generates pools of money for use in bingo games by deducting a percentage of the amount used to purchase bingo cards (in the present invention, virtual bingo cards). Each bingo game automatically enrolls active players in one or more bonus games, exemplified by "4 corners," where the amounts to be given away to players as bonuses are calculated to be equal, over time, to the amount taken in from players buying bingo cards. The house has no stake in the bonus awards.