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You have a good eye for awesome anime, but once again, NHK is quite unique and probably the best of its small niche between psychological and slice-of-life. No other show even comes close to its greatness.
I'll say Paranoia Agent, but I see you already saw that one and is also darker and more violent.
Steins;Gate, is a good sci-fi with a similar feel, comedy, and craziness. I see you haven't watched the sequel yet, so you may want to try that. I made a guide for that.
Tekkon Kinkreet, this is quite psychological, but also very violent & crazy. It has an amazing use of the camera and a very different art style that marches the mood of the story.
Tokyo Godfathers, on the other hand, I wouldn't exactly call this psychological, but it definitely has "troubled" people in it and the same type of comedy/mood than NHK. The creator is responsible for some of the most famous psychological shows and movies, I guess this was his take on comedy.
Penguindrum, is quite unique too, but not so much for the psychological parts, what makes it unique is the symbolism that tells half of the story visually. They will ponder some questions in the dialog and give you the answer through the visual backgrounds for example, so you can interpret it yourself. After watching this, you may be the one with the psychological issues, lol. There is a blend of different styles through the animation and it also changes from comedy to dark drama quite drastically throughout the story. It's a hit or miss kind of show, and what tends to make the difference is how easily you can interpret the symbolic meaning of the story.
ReLIFE, has similar characters to NHK, but in a high school setting that makes it very predictable and similar to so many other shows. It is still enjoyable because it has a good execution, but it's also more comedy/slice-of-life/romance than any of the other ones on this list.
Sayonara, Zetsubou-Sensei is another hit or miss show that many people like because it has a similar style to the Monogatari Series (it's made by the same studio). It tries to be psychological and comedy. I personally didn't like it and drop it in the 4th episode. But you may want to try and see if you find it more enjoyable.
Can you explain what you like/dislike of the shows? That will make it easier to understand what you are looking for.
Enjoy! Let me know how you like them.
LoL, I see you haven't watched these:
Yes, those are great gambling animes, I'm sure you'll probably like Legendary Gambler Tetsuya which is something in between Akagi & Kaiji. Unfortunately, this is as far as we go with gambling shows. I wish they continue both Akagi & Kaiji! Tetsuya does have a proper ending.
You may also like shows like Gantz & Alice in Borderland, although they are not exactly about gambling, they are kind of gambling with their lives as they are forced to survive in deadly games.