A method of awarding wins for game play comprises determining winning outcomes from all possible outcomes of game play and assigning at least one of two different types of awards, such as either or both primary and secondary credit awards, to each winning outcome. Preferably, the winning combinations and associated awards are selected so that, when assigned to a secondary event, the outcome of the game may be represented as the outcomes of a secondary event. In one embodiment, the outcomes of a Class II game, such as bingo, are represented by outcomes Class III type event, such as the game of slots. In accordance with the invention, the representation of the game outcomes mimics the frequency of wins and the payouts associated for those wins in a true Class III game, including as dependent upon the size of a player's wager.