It's fluffier and more disposable than I'd expected, but I still quite like the show. It's nice. I enjoyed it. It's just not doing much with its premise or indeed really going anywhere.
It's set at Tennogofune Academy, a super-prestigious private school where Class 7 is unlucky. They accept candidates just because of their bad luck. They even verify this by hiring private investigators to go through your background and learn all your embarrassing secrets. It's not clear why they do this. Everything about Tennogofune Academy is a bit vague, although we can tell that they're super-rich and employ robot rabbit butlers called Timothy. (These might be remote-controlled by a human girl, though.) They even have James Bond Supervillain Underground Bases for luck-training purposes, with one in ep.3 that's 400m down and then an even deeper one in ep.8 for which you descend a full kilometre. By the time we've hit Timothy's student-grabbing spaceship in ep.11, the show's not trying to maintain even a veneer of credibility and is clearly just a convenient excuse for gag situations.
One also worries about the Class 7 students' academic futures, since the only thing you ever see them doing is happiness training. What about normal schoolwork? Admittedly the start of ep.8 suggests that they have regular classes too, but that training must eat lots of their time.
Personally I'd have liked to see the show's premise taken a bit more seriously. It's silly, yes, but it can be fun to think through silly things. Is the school genuinely trying to improve these students' luck? If they are, then I'm not impressed with their methods. They're just getting our heroines to do lots of luck-dependent tasks. That's measuring luck, not improving it. Maybe in fact it's just a big ongoing therapy session? Alternatively, has the school discovered some kind of karma balance effect that's making classes 1-6 luckier at the expense of Class 7's unfortunates? A sort of luck displacement. A new law of physics, perhaps? This could have been intriguing too, but again the show's not going there.
Instead the show's just a bunch of comedy episodes. They're not going anywhere. There's no progression. The characters are static, except possibly from a thawing tsundere. However I quite enjoyed it anyway.
The title character is Anne "Hanako" Hanakoizumi, who's like the bad luck nuclear option. If she touches a machine, it will break. If she sees an animal, it will attack her. If any accident is possible, she will have it. What's charming about her, though, is that she's super-energetic, cheerful and thinks she's lucky. She loves animals, for instance, and will always charge towards them just as fast as they're stampeding violently towards her.
Ruri Hibarigaoka is the normal one... mostly. She's a bit shy and sensitive about ways in which she sees herself as lacking. Every so often she'll blush at things. Oh, and the object of her romantic affections is a construction road sign.
Botan Kumegawa is the third member of the main trio. She's from a fabulously rich family and she's polite, kind and beautiful. She only has two problems. Problem #1: poor health. She can collapse at anything, she can't run and she breaks bones all the time. Problem #2: poor mental health, in the specific form of low self-esteem. She thinks she's a worm, a maggot and a worthless waste of obese, ugly flesh. She says things like that a lot, usually while emitting a sinister purple aura.
In some cases (Botan's health and Hibiki's sense of direction), this goes beyond bad luck into disability. These people could fail at anything. It's impossible to lose to Anne at a game, even if you're trying to. Theoretically it's a black comedy. There are people who've found the show a bit uncomfortable. Personally, though, I find it far too warm and cuddly to get that reaction from me, with the show's main message being about the power of friendship. Our heroines might be hopeless individually, but they're actually semi-functional as a group of friends who support each other and don't judge. (No one ever comments on Ruri's unique form of sexuality, for instance. They just accept her for who she is.)
This isn't a show to marathon. It's likeable enough that you could probably do it, but the lack of story or direction would become more obvious. Instead it's best watched as a bunch of nice episodes, with an unusual premise. If nothing else, I'd never seen a series based on this idea before.