Btooom! is a lot like the move Saw. It is (yet another) video-games-become-real-life story, and the premise is that "bad people" are chosen by someone who knows them to get dumped on an island for a life-or-death survival game wherein everyone is armed with bombs. Except that Saw took the scenario to an uncomfortable extreme, thereby much more interestingly making a point. I'm not sure Btooom! even had a point to make.
Story: Anyway, the story was weaksauce, containing no clear thematic direction, and coming to very little resolution at the end. We supposedly see the main character come to grips with "how bad he was" in his life prior to being dumped on the island, and then he "becomes strong" to protect a girl.
I say supposedly and use quotation marks because I know that was the intent of the writer, but they didn't pull it off in a believable enough manner. The main character, who was a NEET in his previous life, was attractive and athletic--which to start with is fairly unbelievable. To top it off, his patterns of jerkiness, niceness, and the eventual resolution he makes to protect Himiko and get off the island didn't make any sense based on his actual experiences. Furthermore, Himiko's role in the story only served to feed some nonsense about how getting a girlfriend will magically cause people to become normal members of society.
If the story had gone further in a direction of "these people only seem like jerks to others around them because Japanese culture is XYZ and none of them deserved to be on the island," I probably could've bought it a lot better. As it was, I was never really engaged with any major theme or question.
Characters: I really had trouble relating to them, particularly the main character. There was nothing about him that made me feel sorry for him, and I would say the same for most of the other one-dimensional characters.
Overall, this was a frustrating anime to watch. I think it tried. It wasn't quite bad enough to make me give up on it, but it certainly left a lot to be desired.