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Three Point Shot is more or less impossible to describe without spoiling New Danganronpa V3, so I won't even try. As such, be advised that this review will spoil the game.
The fic diverges from canon when Kokichi, by throwing a shot, helps Shuichi realize that Kaede didn't kill Rantaro, and expose the true culprit and mastermind, resulting in the killing game continuing with different motives, victims and killers. Considering that Kaede's death was the plot development I hated most, I consider this a very welcome change. If you disliked the ending, though, you're out of luck- Danganronpa's still a TV show in this fic.
Most of the characters are handled fairly well, particularly those who live longer than in canon (obviously Kaede, but also Ryoma). The romance between Shuichi and Kaede is decently done, particularly rebuilding their trust in one another after Kaede's murder plot. That said, I'd probably have killed off Shuichi, since he still ends up doing most of the work in solving the class trials, making the fic come off as a bit too similar to canon in that regard. The Kaito and Maki couple was also done well, while giving it a somewhat different outcome than in canon, and it was nice to see Kaede and Maki developing a friendship of sorts.
Unfortunately, there are a few characters who aren't handled as well(Gonta, Tenko, Tsumugi and Kiyo), but I can't elaborate in the main review without spoiling the fic. The most I'll say outside of the comments is that since this group includes at least one murderer, attempted murderer and victim, these problems do noticeably impact the story. This may be because the fic has a challenge similar to System Restore- coming up with plausible and in-character reasons for characters who weren't killers in canon to kill someone in the fic.
Speaking of murder mysteries, one problem is that the second and third murders are relatively simplistic. In canon, most of the murderers who had planned things out in advance, and even some who hadn't, had elaborate setups to kill their victims while disguising their own actions. Uncovering how the murders happened is an interesting process, one that often allows the spotless to discover which person had the talent or opportunity to pull it off, so it's unfortunate that the mystery solving element of this fic is a bit lacking.
TPS also struggles in the technical aspect. The author isn't all that good at writing dialogue or doing descriptions of settings or thoughts, although the executions are nicely done. Game mechanics are included when they'd be cumbersome- the Closing Argument works well as a summary of the case, but Rebuttal Showdown and the others feel too much like you're playing a game, rather than reading a fanfic.
All in all, it's a good fanfic, but I'd hesitate to call it Better Than Canon.
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