The present invention relates to a bonus scheme for a gaming device which involves a terminating symbol moving with respect to a player symbol. The game causes both symbols to visit new locations along a path. The game successively moves each symbol a certain number of locations. As the symbols advance, the player gains various awards and bonus values associated with the locations visited by the player symbol. The bonus round terminates when the terminating symbol catches the player symbol. This type of bonus scheme incorporates a chase or pursuit concept and increases player excitement and joy.