Abstract: A game set for simultaneously playing at least two interactional games on a single chessboard which comprises two or more subsets of pieces wherein each piece in each subset has a different size than the corresponding piece in the other subsets and is fractionally shaped in order to combine with at least one other piece from any other subset on a single square of the chessboard. The game in which a particular piece is currently operating is indicated by a color-coded ring insertable over a stub projecting from the top of said piece. The base of each piece is tierce-shaped with at least two adjacent sides defining vertical planes intersecting each other at 120.degree. whereby at least two bases can be contiguously placed in a circular pattern on a single square of the chessboard.