A subgenre of Psychological Thriller. The genre goes: a very intelligent protagonist, who we will call Alice, finds herself faced with some kind of pressing problem or overwhelming enemy (let's call it Bob), usually a problem which she can't possibly defeat by brute force. Alice attempts to solve the problem primarily with the power of her own intellect. This is fun to watch both because of the tension in figuring out whether Alice can outsmart Bob at all, and also seeing how she does it: what clever plan she uses to defeat Bob.
Often, the protagonist finds herself in the possession of a supernatural power, giving her an asymmetric advantage against the problem. Similarly, often the enemy will be a government, The Mafia, or some other large entrenched organization with the ability to not only use force but to use force on a scale that the protagonist couldn't possibly match alone.
If the protagonist does have a supernatural power, it will have very well defined rules, so that the protagonist can exploit those rules in her clever plans. Usually the genre is full of The Plan in all its many varieties to the point of Gambit Pileup. May have a Science Hero or Guile Hero.
- Death Note is a pretty classic example, where a very smart protagonist with a magic notebook that kills people dedicates his life to solving crime by killing every single criminal. His foe is the world's greatest detective who has to figure out the notebook's rules and stop him.
- Code Geass is another classic example, where a very smart protagonist with the magic power to give anyone a single irresistible order dedicates his life to rebelling against the Evil Empire that's conquered Japan.
- In ERASED, the protagonist is not especially smart, but since he does have the ability to go back in time, he has significantly more information than other people around him. He uses this power to solve a series of murders that occurred around him when he was a little kid, and since his 29-year-old mind is in his 11-year-old body, he's constantly being underestimated.
- In Akagi and Kaiji, both by the same author, the protagonists are geniuses at gambling specifically. They're mostly solving the problem of not having any money and/or owing large amounts of money to the Yakuza.
- In Aldnoah.Zero, the protagonist Inaho fights a Martian invasion of Earth by outsmarting each of their Humongous Mecha as they deploy them.
- Liar Game features characters playing the titular game, a tournament where participants must use psychology to outsmart others in random, deception-based challenges to win money and avoid being forced into debt. The protagonist turns the conflict against the Game's organizers, finding ways to clear the debts of all participants and figuring out the Game's purpose with the help of her genius partner.
- In The Promised Neverland, the three smartest of a group of children raised for their intelligence discover that they are really being raised as cattle, and must outsmart the careful planning of their "Mom" and caretaker Isabella, a genius in her own right, to escape.
- Attack on Titan takes on shades of this very early on and rolls with it. The protagonists' powers are well-defined through experiments and antagonists have a tendency to pull out new ones every so often. Even fights will usually hinge on calculated gambles and reverse psychology. This is perhaps best demonstrated by the massive fight of the recently concluded story arc, which included such plays as the enemies nuking a city using their preestablished powers while the protagonists get around them via trickery and attrition.
- Ajin is a solid example of this, with every fight scene involving the immortal characters being a collection of tricks derived from the basic rules of their abilities. The squishy and killable human cast also doesnt disappoint in how they attempt to get around the immortal Ajins tricks, and overall conflicts are extremely detailed and rule-defined, making awesome moments all the greater when they exploit some facet of the in-universe supernatural.
- When one of the oxygen tanks on the Apollo 13 command module explodes, a team of NASA's best scientists must devise a way to keep a crew of three men alive with the resources to support two on the lunar module until their trajectory brings them back to Earth.
- Megamind heads into this territory when Titan goes on an angry rampage and relentlessly tries to kill Megamind with his Flying Brick powers: Megamind has to find lateral-thinking uses for the gizmos and gadgets he currently has on hand to stay one step ahead of Titan, as he knows he'll die the moment Titan catches up to him.
- Jules Verne's Eight Hundred Leagues On The Amazon: while most of the book is almost entirely a documentary on travelling down the Amazon, the final part is about a judge frantically trying to break a code in order to prove the innocence of one of the main characters. He succeeds just in time.
- Edgar Allan Poe's short story The Gold Bug has one of the main characters going through a pretty extensive analysis of crypto-graphical methods in order to break the encoded message that came with the titular device and hopefully solve the story's mystery.
- The Martian: The book and movie adaptation have No Antagonist other than the unrelentingly lethal nature of Mars trying to kill stranded astronaut Mark Watney and him trying to think his way out of every problem that appears in his attempt to survive (and later escape) Mars. (The book dives pretty deeply into the breakdown of his every idea in how to survive, because it is mostly written as Mark's log entries.)
- In Alfred Bester's The Demolished Man, the protagonist is a brilliant businessman who commits a murder and finds himself in the unenviable position of having to outwit a telepathic detective. It's almost like Death Note in reverse with the good guy as the one who has supernatural capability.
- The Cold Equations is the struggle of one man to find some way to save a girl's life in the middle of a situation where rocket science (the Fuel Equation, mostly) says that there is no way to save her. Unfortunately for him, as much as he analyzes the circumstances, the more he comes to understand that the science is against him and there is no solution to this peril other than have her Thrown Out the Airlock. As the work's page puts it best, this story was an enforced defiance of Fifties sci-fi that didn't had their protagonists being actual Science Hero material but instead just used the Hand Wave of "Science!" to justify whichever Ass Pull would save the day.
- The main character in Eden Green is a rationalist infected with an immortal needle symbiote. As she works to understand the biology, uses, and steep downsides of the symbiote, she embarks on a mission to find ways to destroy it and her fellow infectees, including a violent psychopath named Tedrin. In the sequel, New Night, characters ranging from slow to average to genius apply their instincts and skills to the aftermath of the symbiote invasion.
- Brandon Sanderson's works are known for their Magic A Is Magic A systems, and powers are always well-defined such that characters can exploit them. A better example of this is host Reckoners series, where a group of ragtag militants use guns, research, and some tech to take down seemingly immortal super humans.