A method for providing a prize to a player. The method includes displaying a plurality of prize identifiers and activating a prize associated with one of the plurality of prize identifiers when a plurality of reward points accumulated towards the prize reaches a threshold of a corresponding prize identifiers. The method also includes determining a first proportion of a plurality of proportions associated with a first prize identifier at a first accumulation rate, and a second proportion of the plurality of proportions associated with a second prize identifier at a second accumulation rate. The first accumulation rate is different from the second accumulation rate.