The commercial pilot was returning from a local flight in his vintage single-engine, bi-wing airplane, which was equipped with a tail wheel. He said the winds were light and variable when he made a normal landing on the asphalt runway. However, during the landing roll-out, the airplane suddenly entered a left turn and the pilot was unable to correct with right rudder and brake. The airplane entered the grass area adjacent to the runway, dragging its right wing tip, before it came to rest up on its nose. Examination of the airplane by an FAA inspector revealed that the tail wheel control cable had disconnected from the spring on the right side, which caused the left side spring to pull the tail wheel to the left. In addition, two ribs in the lower right wing were broken.