An object is to provide a free-entry type of race game apparatus wherewith a player can join at any time. This is a race game that simulates an endurance race in which many vehicles run for a long period of time. The vehicles are continually running on the track (ST 1), from which number a player selects any vehicle at will (ST 3) and joins the race in progress (ST 4, 5). The game is terminated on the basis either of a pass count indicating the number of cars passed (or passed by) (ST 6), or a limiting time (ST 7).