Tension fills the room of a high-stakes poker game in Chicago as the men place their bets. The meek Henry Weems does not belong in this group of gangsters. Henry asks for five new cards and lays them down with a perfect straight flush, winning the $100,000 pot. Mob boss Jimmy Cutrona motions to his henchmen, and Henry is taken to the roof. The thugs toss him off the building, and he falls thirty floors into an open service elevator. Miraculously, Henry pulls himself up onto the street and runs off unharmed.

The next day, Scully arrives in Chicago to meet Mulder. Agents staking out Cutrona saw an unidentified man fall from the roof and walk away. Mulder believes the man may have some kind of healing power. Scully thinks the guy just got lucky. They go down through the service elevator into a basement, where they find a laundry cart that has been broken, as if something heavy had landed in it. Among the towels in the cart is an artificial eyeball. Mulder and Scully track down their suspect through an appointment he made to get fitted for a new prosthetic eye. As they enter Henry Weems' apartment building, they are approached by Maggie Lupone shouting for help. Her sink is spraying water and she can't find Henry, the building superintendent. She urges her young son, Richie, to go back to bed. In an attempt to assist her, Mulder breaks the valve and causes more water to spurt from the sink. Suddenly, the floor gives way from all the water and Mulder drops into the apartment below -- where Henry Weems has been hiding.

Mulder returns the artificial eye, and Henry discounts any dramatic description of his fall. He says it was a lucky break. Henry's hobby is constructing complex, Rube Goldberg-like machines that perform simple tasks and Mulder admires his work. Henry admits that he lost all of his poker winnings but refuses to testify against Cutrona. Scully tries to persuade him that Cutrona will go after him. "I'll take my chances," he shrugs. The agents leave and narrowly miss one of Cutrona's hit men as he enters the building. Mulder realizes he dropped his car keys and buzzes Henry. When they hear gunshots, Mulder and Scully rush back to Henry's apartment. Henry has disappeared, but the thug is dead, suspended by the swirling ceiling fan.

Mulder comes up with a complex theory of how the assassin was killed by a series of events that coincidentally occurred in the apartment, much like one of Henry's contraptions. Scully chalks it up to dumb luck, but then notices Richie in the doorway. Seeing that he is sick, she leads him back to his bedroom. Richie shows Scully the Goldberg device that Henry made for him when he was in the hospital for liver disease. He tells her that Henry always says that everything happens for a reason. Scully reports back to Mulder that the boy doesn't know of Henry's whereabouts. She speculates that if Henry was really supernaturally lucky, then he would be out playing the lottery. Hiding in the air vent, Henry hears their conversation. He sneaks out to visit with Richie when the agents depart.

Going over Henry's file, Mulder surmises that Henry's lucky streak began when he was the lone survivor of a plane crash, but he has since gone underground. Only recently has he tried using his lucky fortune. Henry slips out to buy a scratch-off lottery ticket and wins $100,000. However, when he learns that the payment is spread out over months, he tosses it into a garbage can. Another man in the store grabs the ticket, despite Henry's pleadings to throw it away. The man is immediately hit by a truck. When Mulder and Scully investigate, they figure out that Henry had heard their conversation about the lottery ticket. They separate and search the building. Mulder finds Henry in the air vent and holds him while he calls Scully. As he dials, another of Cutrona's gunmen arrive and fire a shot at Henry. The bullet ricochets off Henry, grazes Mulder's arm, and bounces around before it lands in the chest of the thug. Scully arrives in the room just as the hit man drops, not believing that she's seeing Henry unharmed.

Later, Mulder's wound is dressed at the hospital, where he tests Henry at playing cards. Henry draws the highest card every time, confessing that he is extremely lucky and that other people suffer. This is why he keeps a low profile. He says that he tried to get $100,000 for a liver transplant for a new experimental treatment for Richie's liver disease. Although Henry's life is in danger, Mulder believes that his luck will save him, and he allows Henry to leave. Scully pulls one last card and draws one higher than Henry's. Mulder is alarmed by this and runs after Henry, who is also being followed by one of Cutrona's men. Henry gets hit by a truck, but survives. Sensing that his luck has run out, Henry agrees to testify against Cutrona. Richie becomes seriously jaundiced and is taken to the same hospital. His mother Maggie goes to follow the ambulance, but is kidnapped by the mobsters. Henry knows that Maggie was taken to prevent him from testifying, so he goes to speak to Cutrona himself. Cutrona has him brought to the basement where Maggie is being held captive. As the men raise Henry onto a crane, a series of mishaps ensue that kill the gangsters and release Henry. Mulder arrives with the police to find Cutrona dead, and Henry and Maggie saved. It turns out that Cutrona's rare blood type is a perfect match for Richie's, and Richie gets his transplant after all. Henry was right when he said that everything does happen for a reason.