The pilot of the aerobatic, tailwheel-equipped biplane planned to attend a fly-in event at the destination airport. As he overflew the 2,500-foot-long by 60-foot-wide private turf runway, he noted that numerous airplanes were parked along its left side, and elected to favor the right side of the runway during the landing. During the landing roll the pilot felt a "tickle" in the control stick, and the airplane veered right into the tall grass and berm located along the runway's right edge. The airplane subsequently rolled left and right, striking both wingtips on the ground in the process, resulting in substantial damage. The pilot reported that there were no mechanical malfunctions or failures of the airplane that would have precluded normal operation.