When must players shuffle their decks in a tournament?

Players must shuffle their decks at specific points during a tournament to ensure fairness and to comply with the rules. The requirement to shuffle before presenting a deck for a deck check helps to verify that the deck has been randomized properly and is not in a specific order that could provide an unfair advantage. This is an essential part of maintaining the integrity of the game.

Additionally, players are also required to shuffle their decks after revealing their opponent's deck. This is important because revealing an opponent's deck can alter the perception and strategy of how each player approaches the game. Shuffling the deck after this occurs ensures that the information revealed does not influence the order of the cards.

Therefore, it is necessary for players to shuffle their decks before presenting for a deck check and again after revealing their opponent's deck to maintain the randomization of their card order throughout the tournament, making choice C the correct answer.