1. A computer-implemented method of conducting wagering games on a wagering game system, the wagering game system including one or more input devices, one or more display devices, and one or more processors, the method comprising: initially awarding, via at least one of the one or more processors, a plurality of plays Y of the wagering game and a predetermined plurality of attributes X, the plurality of plays Y including play Y 1 and play Y 2 and the predetermined plurality of attributes X including attribute X 1 and attribute X 2 ; displaying on at least one of the one or more display devices a plurality of randomly selected symbols associated with each play of the plurality of plays Y; randomly assigning, via at least one of the one or more processors, all of the predetermined plurality of attributes X across the plurality of plays Y such that each of attribute X 1 and attribute X 2 is assignable to play Y 1 or play Y 2 , each attribute increasing the expected value of the play of the wagering game to which the attribute is assigned, the expected value increasing from a first value to a second value, the first value of the expected value being in the absence of the attribute and the second value of the expected value being in the presence of the attribute; and in response to assigning all attributes of the predetermined plurality of attributes X across the plurality of plays Y, including the first attribute X 1 being assigned to either of play Y 1 or play Y 2 and the second attribute X 2 being assigned to either of play Y 1 or play Y 2 , executing, via at least one of the one or more processors, the plurality of plays Y, each play having an expected value.