The private pilot was receiving instruction to become familiar with his newly acquired tailwheel-equipped airplane. After practicing some standard flight maneuvers at altitude, the pilot returned to the departure airport to practice full stop landings and takeoffs. On the fifth landing, the pilot made a three-point touchdown and rolled straight ahead. During the rollout, the airplane suddenly swerved to the right. The CFI saw the pilot had already applied full left corrective rudder and added left brake to try and correct the swerve, but the application seemed ineffective. After the CFI applied right brake to slow the airplane’s departure from the runway, the airplane pitched over on its nose, then over onto its back, coming to rest in a snow bank bordering the runway. The top of the rudder sustained substantial damage.