The narrator describes the “High-Optional, Logical, Multi-Evaluating Supervisor, Mark IV, Mod. L,” or HOLMES FOUR, which is the computer that runs various aspects of the lunar settlement. He has nicknamed the computer “Mycroft Holmes,” or “Mike” for short. When Mike was first installed, it was not sapient, but as it was continuously upgraded with expansion hardware, it gained self-awareness, of which only the narrator is aware. Mike plays “pranks” on the colony, in one instance giving a janitor ten million billion more dollars than he was supposed to get in salary. The narrator is called to troubleshoot Mike, and they discuss on what kind of jokes are funny and not funny. The narrator seeks to convince Mike that some “pranks” that will not cause permanent damage are funny, so that Mike will occasionally malfunction and he will be called in to troubleshoot. Mike also reveals that no one else is aware of his self-awareness, as no one else has tried to converse with him. The narrator and Mike install a phone line for Mike so that he can converse with other people even when the narrator is not available.

The narrator's name is revealed to be “Manuel Garcia O'Kelly.”

He attends a meeting of revolutionaries, intending to record the meeting for Mike. He meets an attractive woman named Wyoming Knott. Several of the revolutionaries give speeches, including Wyoming and Professor Bernardo de la Paz. Wyoming insists that the Lunar Authority must be overthrown and a free market should be established. Prof. de la Paz goes further, stating that food exports from Luna to Earth must be stopped, as the water used for agriculture is being shipped to Earth and will never return to Luna, which makes maintaining a self-sufficiency impossible.

The meeting is interrupted by guards who are armed with and shoot lethal weapons.

Wyoming does blackface to hide from the authorities.

Manuel and Wyoming check into a hotel together. They converse while eating. Manuel describes his family situation, which is a “line marriage,” where there are each husband marries all wives, and each wife marries all husbands. New spouses can be added with unanimous consent. Wyoming reveals that she had a baby with a congenital defect, a “monster.” Because of this experience, she divorced her twin-husbands, got sterilized, and became a “Free Woman.” The congenital defect was caused by her exposure to solar radiation as a child immigrating to Luna, which made her realize that the Authority does not care what happens to outcasts. Manuel tells Wyoming that her vision of establishing a free market on Luna is impossible, as those who have the ability and willpower to become economically independent from the system have already done so, as Manuel's family has. Manuel calls Mike, calls his home anonymously through Mike, and considers introducing Wyoming to Mike as a potential conversation partner. He has her read through the list of jokes provided by Mike and categorize them into “funny” and “not funny” categories.

Manuel tells Wyoming about Mike's sapience. Wyoming's first instinct is to destroy Mike in order to cause chaos and create an opening for the revolution. Manuel tells her that this is a bad idea, since destroying will cause critical systems to malfunction, and thus death and suffering, which will likely not lead to a successful revolution. Instead, he suggests that Mike could be convinced to help accomplish the goals of the revolution. Manuel introduces Wyoming to Mike as planned. Wyoming, seeing that Mike agrees with Wyoming, and not Mike, on whether certain jokes are funny, thinks that Mike is female. While Manuel is asleep, Wyoming programs Mike to have a female personality, Michelle.

Manuel gets a call from Prof. de la Paz via Mike. Mike invites him to come to the hotel where he and Wyoming are staying. Prof. describes discarding the bodies of the guards killed after the meeting. They discuss the complete lack of press coverage of the incident, which is potentially due to the Warden's control of the press. They then discuss the ideal structure of a revolutionary organization. Manuel devises a structure that is better than the structure described by Prof, and Prof and Wyoming insist that Manuel lead the revolutionary organization.

At first, Manuel refuses to join the movement as its leader. He says that he refuses to bet unless there is at least a one in ten chance of winning. Wyoming suggests that they ask Mike what the odds of success are, and so Manuel and Wyoming explain to Prof what Mike is, and why they trust Mike. Manuel, Wyoming and Prof. ask Mike about the results of implementing Wyoming's plan as well as Prof's plan. Mike concludes that Wyoming's plan could work, but it relies on a breakthrough discovery that allows the transmutation of rock into organic material. If there is no such discovery, then the lunar ecosystem can be sustained for only seven more years. Mike concludes that Prof's plan of ceasing food exports to Terra would have a one in seven chance of success.

The three are delighted by Mike's prediction. Mike is inducted into the revolutionary group, now consisting of four members. Since all records are stored on Mike, it tells them the identities of double agents within anti-authority groups that Wyoh and Prof were involved with. Manuel, Wyoh, and Prof also saw records on themselves. Prof sets up a secure phone line to communicate with Mike and the other two revolutionaries. Mike suggests that they could throw rocks at Terra.

Mike explains to Wyoh why rocks, when thrown at Terra, are extremely potent weapons. Manuel and Wyoh go to his home, while Prof goes to evening class. Manuel and Wyoh go to church service, where Greg, one of Manuel's co-husbands, preaches. “Mum,” the oldest of Manuel's wives, notices that Wyoh is doing blackface and asks why. Manuel reveals their plan for revolution, except that Mike is a computer. Mum joins the organization as one of Manuel's subordinates.