Abstract: A gaming apparatus and method are provided which utilize a number generating device for generating numbers which are statistically predictable in the long run. The device includes a plurality of screening devices arranged in vertically spaced relationship to form n levels and including holes therein through which spherical objects, such as marbles fall, when dropped through the uppermost level. The holes are arranged to provide a Binomial distribution of the objects in receptacles associated with each hole of the n.sup.th level screening device. A number is associated with each receptacle and scoring is based on multiplying the number of objects in a receptacle by the number associated with the receptacle. Spinners determine the number of objects to be played and the target value to be reached during a turn in order to amass a positive score.