I loved Liar Game and having recently read till the latest chapter of Kakegurui and Usogui, I really feel the need for more.

I'm not sure if I can explain the essence of these mangas well, but basically the protagonist (the one who is actually solving puzzles) should be someone who is almost unbeatable and unrivaled in intellect. Having a series of psychological games/traps/puzzles would be great, and the protagonist can participate for either noble or selfish reasons, but he/she should still win. I just love these psychological games - whether it is learning how to cheat the cheater (in Usogui and Kakegurui) or simply how to beat out the other opponents (Liar Game).

Any recommendations are welcome!

Nulla in mundo pax sincera
"Always go too far, because that's where you'll find the truth." - Albert Camus

One of personal favourite genre(?), this. Unfortunately, there are very few manga like your examples, and even fewer that have/will be scanlated to completion.

One Outs -- You may think this is about baseball, but really it isn't. It's a high-stakes mind game with the baseball scene as its stage. Regular scanlations are only available after v10 c81, which is where the anime ends. The anime follows the manga storyline pretty faithfully (deviating only in the last 10 minutes or so of the last episode), and it's even more exciting than the manga, so I recommend it.

Speaking of One Outs and Liar Game, several other Kaitani Shinobu manga would fit: particularly Muteki no Hito and Winner's Circle e Youkoso. Neither of them are scanlated, though.

Tobaku Mokushiroku Kaiji and its sequels are pretty iconic. The first series isn't fully scanlated because the first Kaiji anime covers its story. The next parts are either scanlated or in the process of being.

Tobaku Haouden Rei and its sequel, by the mangaka of Kaiji.

Tomodachi Game is more 'psychological trickery' than actual games, but it reminded me of (a shounen version of) LG.

Shion no Ou -- Maybe. It's just shougi, though the stakes are higher than that of a typical match.

Likewise, a lot of high-stakes gambling series like Akagi may fit, but unless you have at least a passable knowledge of mahjong they lose all their fun. I had to give up after a few volumes, myself, since I know nothing about the game and it's difficult to learn just by reading Wikipedia.

Tatoe Hai ni Natte mo -- Maybe. I haven't started reading it yet, though.

Doreiku - Boku to 23-nin no Dorei, perhaps. It's a bit more on the crazy horror side, though.

Gamble Fish -- Dropped this because I can't stand harem ecchi, but I think it fits.

And for your wishlist (unscanlated/dropped by scanlators), unless you can read Japanese:

Acma:Game
Gorudiosu no Musubime
Riman Gambler Mouse
9 no Puzzle to Mahou Tsukai

Thank you for these suggestions! I have read all the scanlated manga Kaitani Shinobu (and adore them), along with Shion no Ou. I guess Kaiji is the one I'll start with then. 🙂

Nulla in mundo pax sincera
"Always go too far, because that's where you'll find the truth." - Albert Camus