When I was reading reviews of this when looking for anime to watch, no one seemed to think it was great, but there was general agreement on it being very funny. (Also, boobs.) I picked it up and I disagree with the consensus. It is in fact great.
Our good luck girl is Ichiko Sakura, who thinks her life is perfect. She's clever, rich, pretty, super-popular with the boys and lives in a mansion with her own personal butler. In fact, life's so good for her that she's throwing the world into karmic imbalance. She's a happiness vampire. She doesn't know it, but she sucks the good luck and health out of everyone around her, to such a degree that it could endanger their lives.
"Good luck" is a complicated concept in this series, by the way, beyond any single word in either English or Japanese. It includes health, happiness and material fortune, but ultimately it comes from people and you need a balance of both happiness and unhappiness in your life. Ichiko's "good luck" has made her callous, greedy and insufferable. She has an appalling personality. She thinks altruism is for suckers and she's capable of going through agonies of anti-conscience if ever tempted to do something to help someone else. In contrast, "misfortune" (in this show's terminology) can unite people, make them empathise with others and hence be the source of a more profound kind of happiness.
Ichiko is, despite first impressions, a conflicted and broken person with misery buried deep underneath her happiness. It's as if there are two of her. There's a good Ichiko inside the unpleasant one. It's just that her self-defence mechanisms include denial of any noble motive and an active pleasure in being smug, bitchy and obnoxious.
Charged with rectifying this situation is Momiji, the Poverty God (aka. Bimbougami), whose personality might conceivably be worse than Ichiko's. She's lazy, rude, childish and mean-spirited. Her assigned task is to suck out Ichiko's good luck and condemn her to a life of drudgery and misery, which she sets about with glee because she took a dislike to Ichiko just from her photo. She loves infuriating Ichiko in any way imaginable, which is saying a lot because she's a deity with superpowers. Her favourite activity is stabbing Ichiko with a happiness-sucking syringe big enough to use on whales.
It's war. This is very, very funny.
What makes it great, obviously, are the two leads. They're complicated. They're both capable of being monsters, but they also both have goodness hidden deep down. Ichiko gets the big decisions right. If something really matters, she'll put herself on the line for you. It's just that she'll have probably stabbed you in the back earlier, either from callousness or indifference, plus of course doing the right thing means wrestling with her anti-conscience. Mind you, she's vulnerable if you can get under that emotional shell of hers.
Meanwhile Momiji is technically trying to do good. Ichiko's good luck is a threat to everyone close to her. Momiji's effectively turning herself into Ichiko's conscience, albeit in a massively dysfunctional way.
Sometimes the show's just comedy war, which is funny. Look at everything Ichiko does to a puppy in episode 4, for instance, while Momiji's unleashing enough wacky schemes to make Ichiko almost look like the underdog. The two genuinely can't stand each other and it's no holds barred... except that it's not, because sometimes they'll fight themselves to a standstill, call a temporary truce and just hang out as if they were friends. They could almost be a (dysfunctional) couple. In the original manga, one of Momiji's techniques for annoying Ichiko included acting like her girlfriend. You certainly wouldn't expect either of them ever to find such a well-matched opponent.
Besides, underneath, they're both good people. Quite often, this show will dig past the surface comedy into powerful emotional territory. This is outstanding. The last two episodes go places I hadn't expected, for instance, although of course it won't end in hugs and kisses.
The supporting cast aren't as interesting, although Ranmaru's great when she shows up halfway through. She's a butch, violent thug who's simple-mindedly loyal and has hidden reserves of girliness. She's lovely. She also ends up being the only person who can get under Ichiko's armour. Meanwhile the men tend to be colossal perverts, with Bobby the monk being super-lecherous and Momo'o Inugami being a masochist who takes pleasure from physical abuse. (He's come to the right place.) On the other hand, there's also a family of children headed by their big brother, Keita Tsuwabuki, who have no money and are everything Ichiko isn't.
There's also a ninja girl, Nadeshiko Adenokouji, and her butler. They appeared late in the manga and only appear in the anime after each episode's end credits. If you don't know that, you might get puzzled about what they're doing there.
This can be a deep show, but it's also great at being shallow. It made me laugh and laugh. In episode 9, for instance, we discover that Ichiko might be the worst cook in anime. That's a big claim. Anime is full of characters (usually female) whose cooking will cause vomiting, hospitalisation or physical transformations. See Lum in Urusei Yatsura, for instance. Nice girl. Bad housewife. Ichiko, though, can make food that screams like the damned in hell and the only person to eat it goes through hilariously protracted agonies before departing this mortal realm. Beat that.
I also appreciate the lack of fanservice. The show flat-out refuses to do panty shots, while Ichiko's boobs are sensibly sized, despite all the dialogue about their supposedly gargantuan proportions. (Momiji is like an ironing board.) They'd be big in real life, but there are plenty of anime where Ichiko would be the small-breasted one. Admittedly there are episodes (4, 11) with extended nudity, but that's because bitching and battle scenes are funnier when everyone's naked. Besides, the naughty bits are censored and it's equal-opportunities exposure, with Strategic Black Scribbles for the men and lots of gratuitous beefcake from Keita.
The end credits have fanservice, mind you, as Ichiko and Momiji do cosplay. (It's fun, not offensive.) However I adore the accompanying song, which is so much better than the opening that I don't understand why they didn't switch them. (For the final episode, they do.) Obviously, it's normal in anime to try to draw people in at the opening credits, not the closing ones. Anyway, the song's called "Love Riot" by HAPPY BIRTHDAY and I swear it's being sung through the singer's nose.
Warning: don't listen to the English dub. Personally I never do anyway, but I've heard that this one is particularly bad at switching between the show's two modes (emotional depth vs. outrageous, broad comedy) and undermines the serious side of the show. My theory is that this explains those luke-warm reviews I mentioned.
In short, it's great. I love it. I want a second season. Yoshiaki Sukeno's completed the manga, so they'd be able to finish the story. Love the characters and their relationships. Love the deeper stuff. Love Ichiko and Momiji waging war on each other. I'm terribly fond of this one.