 If you liked
Kami nomi zo Shiru Sekai
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 ...then you might like
Doubt!
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An anti-social shut-in is given the mission to investigate certain girls in order to get close to them. Both protagonists are smart high school students who are good at analyzing situations and turning them in their favor through various ways of manipulation.
Differences: The World Only God Knows is about the supernatural, has more girls, and takes routes similar to those found in games and visual novels. Doubt is about a realistic setting, has only a few girls, and takes a route that focuses on observation and psychology.
These stories have similar minded protagonists with a mission - getting close to select girls. While Keima uses gaming tropes to predict real life patterns, Ichiru uses observation and psychological tricks on people.
In both stories, the MC:
- starts off secluded from the world
- has to get close to girls for his mission
- reads people to interact with them
- has no interest in anything but the mission initially but eventually changes
- is fallible, takes gambles, and gets caught off guard a few times
Doubt is short but has an open ending, TWGOK is lengthy and sort of ties up looses ends in a weak third act.