Abstract: A gaming apparatus having at least two competing objects each identified by an associated unique set of identification symbols wherein a game is played by positioning the objects in competition as a function of numbers associated with each object. The gaming apparatus includes a random symbol generator generating a random sequence of the symbols. A computer device calculates an independent incremental value (I.sub.x) for each object based on each symbol drawn in the random sequence. Each incremental value (I.sub.x) calculated for each object is a function of the identification symbols contained in the associated set, and each determines an independent incremental progression of play of each respective object. The computer device further computes a position value (M.sub.x) for each object which is a function of the respective incremental value (I.sub.x) for each object, and for each symbol drawn in the random sequence. This position value determines a competing game position relative to any other object.