Well, this looks dandy, doesn’t it?
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I think it’s very smart for the trailer — and perhaps the show — to play up Melisandre’s role, and the role of religion in general, in Westeros. Over the course of the novels, one of the things I’ve come to find most fascinating in them is the duel between the rationality of realpolitik and the rationality of religion. There are a lot of purely rational or strategic actors, both on the state and individual level, in George R.R. Martin’s novels. Littlefinger is probably the most prominent example of that phenomenon: he’s cold, calculating, not particularly attuned towards conventional morality (including killing his wife or making sexual advances on his teenaged ward who happens to be the daughter of the only woman he’s ever loved) if he can find a way to turn events to his advantage. Illyrio Mopatis is motivated less by a desire for power than for profit, to the extent that he’s willing to see an entire continent destabilized to fulfill his aims. Someone like Ayra Stark, who has been essentially abandoned by the Gods, has made vengeance her religion and is extremely tough and strategic in pursuing that goal.
Then, there are the mystics. Part of what makes Stannis Baratheon unpredictable — and thus makes him more powerful — is the fact that he makes decisions that aren’t purely governed by rational strategic calculations. Melisandre’s advice makes him think more than some of his competitors about how the common people of Westeros understand leadership and moral authority, and to take actions like fortifying the wall or going after Ramsay Bolton. The neglect of the wall and the continued empowerment of a psychopath are both stains on Westeros that have major ramifications for both the stability of the realm and the integrity of law in the nation. By trying to address both of those problems, Stannis puts himself and his forces at risk, but he has an enormous amont to gain both strategically and morally from taking on tasks that his rivals ignore. Similarly, the High Septon acts as a wild card, surprising Cersei by reasserting the importance of moral purity and using his power to enforce norms in a way that affects her standing as a rational leader.
In fact, the whole series is really about what happens when you try to assert purely rational governance in a world where fairy tales and Gods reach out into the world and muck up your affairs. It’s one thing to play the Game of Thrones when the rules are stable and the motivations of the actors you’re dealing with are predictable. It’s quite another when dead men walk, dragons return from extinction, and even humans are governed by things other than pure self-interest.