As soon as Lord Stark and Jory are outside the brothel, they're surrounded by Jaime Lannister and a bunch of guys with pole arms. For the old-school D&D players in the crowd, I will speculate that they're either bill-hooks or glaive glaive guisarme voulge glaives. Jaime's on a horse, probably because he thinks he looks good up there. He kind of does, actually. Jory is outraged at this, because Ned is the Hand of the King. But Jaime points out that he was the Hand until a few scenes ago. Littlefinger comes out to demand to know what's going on and Jaime tells him to get back inside and not bother the adults while they talk. Jaime asks if Ned has any idea what happened to Tyrion, and Ned promptly answers, "He was taken at my command to answer for his crimes." That's not even true, but I guess he has to stand up for his wife. And it's time for swords to come out. Boy, the Wolf and the Lion are fighting much earlier than I thought they would. Like, I thought Varys and Illyrio meant that forces were slowly aligning to bring the two houses into inevitable conflict, not that they'd be waving swords at each other before the end of the episode. Littlefinger runs off to call the City watch. Ned warns Jaime that if he kills him, Tyrion will die. Jaime considers this briefly. "You're right. Take him alive. Kill his men."
It's fight time! Jory goes directly for Jaime. And he immediately takes a knife to the eye. Oops! So Jory's dead now. So much for him. Now it's time for Ned and Jaime to fight. It's very fancy, and they're both clearly very good. But before the fight can go on too long, one of Jaime's soldiers stabs Ned in the back of the leg and he goes down. Jaime punches the soldier in the face, because he wanted to prove how great he was. But now that Ned's on the ground, Jaime can look down on him and tell him, "My brother, Lord Stark. I want him back." Jaime and his men leave while Ned lies bleeding on the street.
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