Deck Master K is the Yu-Gi-Oh! The Duelists of the Roses incarnation of Duel Master K. He is available only in the Custom Duels. He uses the same Deck as the player. If the player defeats him, then they can win copies of the same cards that they have in their own Deck.
Deck Master K will also match the same settings as the player, provided they are equal to or above the default settings of a duel. If you lower the Life Points for the custom duel below 4000, Deck Master K will still have 4000 Life Points. Same for setting the summoning level below 3.
If the player has a memory card with saved data from Yu-Gi-Oh! Forbidden Memories in slot 2, they will Duel Deck Master T, if it is a PlayStation 1 memory card, or Deck Master S, if it is a PlayStation 2 memory card. Deck Master T uses an Exodia themed Deck, while Deck Master S uses a deck full of Egg themed cards, with Goddess of Whim as the deck leader. When beating these alternate deck masters, you get a graveyard slot just as if you beat an enemy in the main campaign, meaning you can earn any cards from those decks that are available in the slots.