In the year L.C.227, the world of Septpia faces great danger. Following the conclusion of a hundred-year war in the world of Tetra-Heaven, the losing side now seeks refuge in Septpia, and their intentions are anything but pure. To protect the innocent civilians, the governments of the world are forced to create a special police force dubbed Another Logic Counter Agency, or ALCA. Comprised of Humans capable of harnessing Logic and the Gods that have allied with Septpia, Logicalist's and Covenanters fight side by side to defend the world.
The story of Luck And Logic follows Yoshichika Tsurugi, a young former Logicalist who was discharged after losing the power of logic at an incident in Hong Kong. Living now with his father and younger sister, Yoshichika is no different from the average civilian. One day though, he met the Goddess Athena, who had found his lost logic. Now capable of fighting for ALCA again, Yoshichika and Athena must work together to stop all who threaten Septpia.
The Luck And Logic Anime aired from December 2015 to March 2016, comprised of 12 episodes.
The anime is one of two projects of "Project Luck & Logic", a multimedia franchise created by Bushiroad, who also created Cardfight!! Vanguard and Future Card Buddyfight, with the participation of five other companies (among them is Dogakobo, the studio behind the anime itself). The other project is Bushiroad's own card game, Luck & Logic. However, unlike typical anime based on a card game, the anime has little to do with the card game and is simply an introduction to the game's lore.
In addition to the main series, a spinoff title called "We Are Luck & Logic Club!" premiered as a series of shorts debuting on the Luck & Logic YouTube channel and also airing on TV prior to each episode of the main series. Set outside of the main continuity, the series focuses on a group of girls who play the card game version of "Luck & Logic" during their lunch club. "We Are Luck & Logic Club!" aired as two mini-seasons (comprising the actual show's full season) for 12 episodes each. The series is set to continue with the debut of "Hina Logi" in Summer 2017.
A yuri spinoff series aired in the Summer 2017 season. Titled "Hina Logi ~from Luck & Logic~", the new Lighter and Softer series follows a new protagonist, Liones Yelistratova, a small-time princess who travels to Hokkaido to join ALCA. There, she enrolls in Class S, and meets many unique classmates and Logicalists along the way, including Nina Alexandrovna who she falls in love with.
Luck & Logic provides examples of:
- A Day in the Limelight: Episodes 3,4,5,6,8, and 9 serve as this for Tamaki, Chloe, Mana, Yukari and Quetzie, Veronica, and Olga respectively.
- A God Am I: Olga adopts an attitude like this after trancing for the first time with Lucifer.
- The Ace: Yoshichika Tsurugi and Olga Breakchild for the Naien Branch.
- Yoshichika is one in the more typical sense. Having worked for ALCA since he was 13, Yoshichika is considered a great Logicalist and born leader. Capable of easily adapting to new Covenanters, he is also the first individual and one of the only two to successfully perform the forbidden Over Trance.
- Broken Ace: Olga Breakchild started as a normal Ace, but slowly became this. Originally said to have unprecedentedly high Logic, Olga joined ALCA believing he would rise to greatness. While his Logic is great and his estimates are typically spot on, his conceited belief that Covenanters were meant to further his own glory led to him being incompatible with all potential Covenanters. Fed up, Olga tried bargaining with captured Foreigners to make covenants, but was still rejected. Granted, Olga also wished to create peace between Foreigners and Humans, his conceited attitude ultimately prevented this. After Lucifer manipulated ALCA newbie Miki Shinobu into releasing the foreigner Enlil, Enlil Transjacked Olga, causing Olga to lose the Logic Card that gave him his logicalist powers. Add to the fact that Olga was a major suspect in releasing Enlil, Olga crossed the Despair Event Horizon and teamed up with Lucifer and he returned said Logic Card. After finally trancing, he proved to be the strongest of all the featured Logicalists, capable of defeating Yosuchika, Tamaki, Chloe, Mana, Yukari, and Veronica all at once. His strength forced Yosuchika and Athena to perform Over Trance, with Olga becoming the second individual to perform Over Trance to fight back, with the two being evenly matched for most of the fight.
- Action Girl: Though all the female Logicalists qualify, Chloe and Veronica best embody this.
- Adorkable: Yukari. The newbie when it comes to Logicalist duties, and a former coach, she enjoys helping out her friends, refers to everyone, whether they are older or younger, as "Senpai", was able to get Quetzalcoatl to Covenant with her just by acting like she usually does, or, as Quetzie puts it, like a miko,and got Quetzie to stay in Septpia just by tearing up.
- Affably Evil: Lucifer. He wants to make Gods and Humans equal so he can control them, and was stated to be the leader in the rebellion that caused Tetra-Heaven's hundred-year war, yet is able to attract legions of followers, all different ages, to aid him in his goal. Olga included.
- Alternate Universe: On first glance, Septpia seems like an entirely different world. However, upon further inspection, many references to Earth's locations such as the Hong Kong Branch of ALCA heavily imply that Septpia is simply Earth, but enhanced thanks to Logic.
- Animate Inanimate Object: The Foreigner from Episode 4 is capable of creating these. Capable of creating Paradox Level 4 entities without a Transjack, these "Foreigners" are actually Grave Markers connected to a tether. Fittingly, the real Foreigner is a Puppet Master.
- Anti-Villain: Olga, episodes 10-12 only. Like many others, Olga was tempted by Lucifer and gave in due to his feelings of Self-Value over not having a Covenanter, and willingly partook in the fight against ALCA and release of the captured Foreigners. Unlike Lucifer though, Olga wanted Humans and Gods to be equal so as to create a better world, and held a sense of honor during his battle with Yosuchika, refusing to attack the others when they went to shield him in an Untranced state. Lucifer however, had other ideas.
- Arrogant Kung-Fu Guy: Olga.
- Authority Equals Asskicking: Vernonica Ananko is the chief the Naien District of ALCA, and as such usually delivers orders from the command center. However, she and her Coventar, Nemesis, are perfectly willing to enter the field and kick some serious ass.
- Awesome Mc Coolname: Olga Breakchild.
- Chloe deliberately attempts to name her logic drives like this. In most cases, it ends up belonging in the Department of Redundancy Department.
- Ax-Crazy: Most of the Destructive Foreigners that come to Septpia are this. Others, like Quetzalcoatl, aren't deliberately destructive, but cause just as much damage in the long run.
- Badass Adorable: Mana and Yukari.
- Mana starts off as an Emotionless Girl, being the youngest Logicalist and an excellent sharp shooter. However, after having her emotional wall broken by the others, she turns into a Shrinking Violet, just as badass, but even cuter. Especially When She Smiles.
- Yukari may not be as badass as her fellow Logicalist's, but she proves effective on the field thanks to Quetzie giving her flight abilities, making her great for reconnaissance, and a great help with getting her allies somewhere extremely fast. Even further when we actually see her Logic Drive. As for whether or not she is adorable, see Adorkable above.
- Bare Your Midriff: Chloe, in her casual clothes and her Trance Form.
- Big Bad: Lucifer.
- Breather Episode: Episode 7 has the characters relaxing at Yosuchika's place and also features Character Development between Yosuchika, Olga, and Athena.
- Cold Sniper: Mana, when tranced with Artemis. She shows little to no emotion when using her sniper rifle.
- Disney Death: Near the end of Episode 10, Utsutsuno Jarno presumably dies in an attack caused by Olga following his Face–Heel Turn when he was told to stop. By the next episode, he's alive and kicking.
- The Dragon: Olga to Lucifer, following the former's Face–Heel Turn in Episode 10.
- Expy: Chloe in her Trance form resembles Ryuko Matoi.
- Face–Heel Turn: Olga undergoes this in Episode 10, becoming Lucifer's Dragon. However...
- Heel–Face Turn: Olga in the final episode redeems himself at the last minute. Lucifer redeems himself as well.
- Fusion Dance: The whole underlying concept of Trancing is that the Logicalist combines with a designated Foreigner called a Covenantor.
- Instant Awesome: Just Add Dragons!: Quetzalcoatl, who goes from being a scary monster to being a Ridiculously Cute Critter to becoming Yukari's Covenantor.
- Jerk with a Heart of Gold: While Olga can come off as a Jerkass at times, he does encourage Yosuchika to reconcile with Athena after he had doubted her.
- Merchandise-Driven: It's based on a new card game by Bushiroad.
- Nice Girl: Athena.
- Red and Black and Evil All Over: Lucifer.
- Sleep Cute: Athena, as noted by Venus.Venus: Athena, your sleeping face is so lovely!
- Stripperific: The female Tranceunions, especially Tamaki and Chloe when tranced with Venus and Valkyrie respectively. This does not go unnoticed by Yoshichika in an exchange with Tamaki in Episode 2, which also reveals this might not be an intended purpose after all (at least in the world of the anime):Yoshichika: Thank you Yurine. (Briefly stares at Tamaki, who then blushes) It's not like that! And it's your own fault for dressing that way!Tamaki: I can't help it. This is Venus' gear after all. It's not like I'm in this outfit because I want to be.