Liar's Gambit

Before leaving a casino with a huge sum of money the owner convinces you to play a series of "card" games in a double-or-nothing proposition. After entering a VIP room to play the card game with the casino owner you realize that the card games are in fact logic puzzles with a card theme. The casino owner gives you clues and hints to understand and "win" each game, but it becomes clear that some clues are lies and others are truths. Can you hit the jackpot and solve each puzzle by discerning which facts you can trust and which are lies?