So... is Binbougami ga! finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 27, 2012
Manga finished: July 04, 2013
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Ichiko Sakura is incredibly lucky, possessing beauty, intelligence, and wealth, all seemingly effortlessly. However, her good fortune comes at the expense of those around her. Momiji Binboda, a poverty goddess, discovers that Ichiko is unknowingly absorbing the luck of others, leaving them struggling.
Momiji's mission is to reclaim the stolen luck and restore balance. She confronts Ichiko, but Ichiko, with the help of an unusual monk, initially manages to fend her off. Undeterred, Momiji gains allies in a teddy bear familiar and a peculiar dog god.
The anime follows the chaotic and comedic struggle between Ichiko, desperate to protect her good fortune, and Momiji, determined to redistribute it. Ichiko's peaceful life is upended as she faces increasingly bizarre challenges in her daily battles against Momiji and her unconventional team.