Methods and apparatus for providing an award based on a multiplicity of game outcomes. In one implementation the invention provides a method for providing a game. The method includes placing a bet by a player, playing of a game to produce a game outcome, evaluating a primary game outcome, paying a direct award if the primary outcome merits it, advancing a bonus accumulator if the primary outcome merits it, and if the bonus accumulator has advanced sufficiently, paying a bonus award to the player and clearing the bonus accumulator.