The current document is directed to gaming dice, including physical dice and virtual dice represented on an electronic display or viewing screen. Certain of the currently disclosed gaming dice have approximately ovoid, prolate spheroid, or ellipsoid shapes that are modified to include planar surfaces. Other of the disclosed gaming dice have angular shapes, including cubes, tetrahedrons, octahedrons, and other regular shapes that are modified to provide nonuniform probabilities of position landings.

A method of weighting a chess piece, comprising the steps of creating a first cavity in a base of the chess piece, and filling the first cavity with a powdered metal. The method also includes the step of creating a second cavity in the base, and filling the second cavity with an electronic sensor so that the piece may communicate electronically with a sensory chess board.

A weighted chess piece, comprising a base having a first cavity and a second cavity therein, wherein the first cavity is filled with loose particles of metal and the second cavity contains an electronic sensor.

A rolling toy to be rolled on a horizontal support surface, for instance, on a floor, having a primary roller and a secondary roller. The primary roller having a tubular-like member extending along a longitudinal axis and at least one annular flange fixedly attached to the tubular-like member and extending outwardly therefrom. The secondary roller is adapted a for rolling motion upon an interior surface of the tubular-like member when the primary roller rotates about the longitudinal axis due to the rolling motion of the rolling toy on the horizontal support surface. At least one of the following includes a helical guiding means: (i) the tubular-like member and (ii) the secondary roller. Thereby, when the secondary roller is disposed on the interior surface of the tubular-like member and the primary roller is set in a rolling motion on the horizontal support surface in a predetermined direction, the rolling motion of the primary roller results in a tilting of the latter. The tilting of the primary roller may result in its standing vertically on the horizontal support surface.