The invention provides a gaming machine having manufacturer-limited parameter values or parameter value combinations selectable by an operator during gaming machine set-up. The parameter values preferably include different maximum pay lines associated with different denominations and are limited to those which have been determined by the manufacturer to provide optimum game play. The different maximum pay lines may be associated with different math models having substantially the same payback percentage values. Subsequent operator selection of the parameter values during gaming machine therefore setup allows the gaming machine having a single game theme or a gaming machine having multiple game themes to be configured with different maximum pay lines for each single game theme. As a result, the player can play a single theme wagering game with a first maximum pay line value and with a second maximum pay line value where the second maximum pay line value differs from the first maximum pay line value.