An interesting fanfiction about Robert Baratheon could involve him making different choices. Instead of relying so much on his advisers, he could start to make more independent decisions. This could lead to different outcomes in battles or political negotiations. You can also play with the timeline. For example, what if he had met Lyanna Stark again after he became king? How would that have changed his relationship with Cersei and his rule? By exploring these 'what - if' scenarios and giving Robert more agency and complex decision - making, the fanfiction can be really captivating.
To make a fanfiction about Robert Baratheon interesting, you can give him new challenges. Maybe he has to deal with a magical threat that the original series didn't show him facing. You could also explore his backstory more. What was his life like before he became king? His upbringing, his first loves, and his early battles could all be interesting areas to explore. Additionally, changing the power dynamics around him can be great. For instance, if some of the minor houses suddenly become more powerful and he has to negotiate with them. This can lead to all sorts of interesting political intrigue and character development.
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