"Luck & Logic" is set in a world where humans coexist with deities from a parallel dimension known as Tetraheaven. The story unfolds in Septpia, a city protected by the ALCA organization, which employs Logicalists—humans capable of forming contracts with deities to combat invading forces known as Foreigners. These Foreigners are rogue deities seeking to disrupt the balance between dimensions.

The protagonist, Yoshichika Tsurugi, is a former Logicalist who retired after a traumatic incident. His life takes a turn when he encounters Athena, a goddess from Tetraheaven who seeks his help to prevent a catastrophic war between dimensions. Reluctantly, Yoshichika forms a contract with Athena, regaining his abilities as a Logicalist. Together, they join ALCA to protect Septpia from Foreigner threats.

The narrative explores the dynamics between humans and deities, emphasizing the importance of cooperation and trust. Yoshichika’s growth as a leader and his evolving relationship with Athena form a central arc. The series also introduces other Logicalists and their deity partners, each with unique abilities and personal struggles. Characters like Olga Breakchild, a stoic and skilled Logicalist, and Mana, a cheerful yet determined young girl, add depth to the ensemble cast.

As the story progresses, the stakes escalate with the emergence of powerful Foreigners and internal conflicts within ALCA. The series delves into themes of identity, sacrifice, and the consequences of wielding immense power. The interplay between logic (represented by human intellect) and luck (embodied by divine intervention) serves as a recurring motif, reflecting the series' title.

The plot balances episodic battles with overarching developments, culminating in a climactic confrontation that tests the bonds between humans and deities. "Luck & Logic" combines action, fantasy, and character-driven storytelling, offering a cohesive narrative that explores the complexities of interdimensional coexistence.