Before we see him we know that he or his men have killed the red-toothed tavern keeper. She was just a woman running an inn. What a shame, and I believe that’s what we’re supposed to feel at recognizing her corpse on the gibbet. Tywin is not nice.
Cool under pressure, Tywin is so focused. He never smiles. Problems thrown at him barely register. He intends to break Robb Stark, and then focus on Stannis. He is the most mentally and physically disciplined person in the story. Diplomacy and persuasion are as much a part of his arsenal as tactics and might. No wonder his children are, at least, intimidated by him and, at most, terrified.
His armor is described in great detail. It’s amazing! I wish they’d included it in the show. Gold, lions, rubies, a heavy cloak long enough to drape the horse’s hindquarters. You can see him glisten from afar. What kind of man indulges in something so practical and yet so artistic? When the battle is mostly won, Tywin rides forward, shiny and majestic, surrounded by banners and spears. It’s epic. The man knows showmanship.
However, he misjudges Robb’s tactics. He calls Robb green, which he is, and assumes Robb will act rashly, which he doesn’t. It’s a great, fist-rising moment of victory for the Starks. Does he guess wrong because his pride blinds him? Is he just unlucky on this day? Or is there something about the Starks — a leadership based on camaraderie rather than dominance — that a Lannister can’t understand?
Well, his success at everything suggests a Three. He’s got it all. An imp child would particularly cause such a man to feel shame. Cersei, a medieval-era woman with a ruthless mind and a willful ambition, would baffle and embarrass him. And Jaime, the golden lion who fights hard in whatever direction his father points him, would please Tywin most.