In Magic tournament play, apart from a some effects that allow players to order the top and or bottom of their libraries, libraries should be random. To achieve this randomness, players are required to shuffle their deck at the beginning of each game and at other points during a game. As mentioned above, the end goal of shuffling is to completely randomize the library. Some techniques, like pile shuffling, can reorder a library but do not truly randomize it. Because of this pile shuffling alone is not sufficient and shuffling by other methods is required.
After a deck is shuffled by a player, it must be presented to the opponent for additional shuffling. (At regular events players can choose to either not shuffle their opponent’s deck or simply cut it.) When shuffling an opponent’s deck you should focus on randomizing the deck as well as making sure that you do not damage cards or sleeves. If you do not believe that your opponent is being careful or is not actually randomizing your deck you can call a judge over to shuffle your deck. However, judges can decline to shuffle decks when requested.
At all competitive and professional events, players must shuffle their opponent’s deck when it is presented to them.