Abstract: A figure unit for a game has a figure disposed on a disc that is secured to a self-righting cup. The disc is connected to the cup by a connection that is concealed within the cup. For that purpose, the disc is provided with a spigot that protrudes down into the cup and engages a socket inside the cup. Preferably the socket is a hollow cylinder that extends upwardly from the cup's bottom and preferably the socket is split longitudinally to form flexible segments that grip the spigot. In one embodiment, an annular metal ring is placed around the socket near the bottom of the cup to limit spreading of the segments when the spigot is engaged in the socket and to act as a ballast weight for righting the cup. To cause the segments to more firmly grip the spigot, a spring clip can be placed around the socket to make the segments clamp around the spigot.