"Cartman's Incredible Gift" is the thirteenth episode of Season Eight, and the 124th overall episode of South Park. It aired on December 8, 2004.
After sustaining a severe head injury, Cartman appears to have the power to see into the future. Park County detectives are quick to enlist his help in cracking unsolved murder cases and Cartman is more than willing to help... for a price. In the meantime, a group of "licensed" psychics cry foul when Cartman refuses to join their ranks.
Cartman attempts to fly by jumping off of his roof with cardboard wings attached to his arms. After falling to the ground, he goes into a short coma, and wakes up in the hospital, where he shares a room with a victim of a serial killer who cuts off the left hands of all his victims. Just as the police are lamenting the victim's death, Cartman manages to guess the hospital food's dinner and a few other obvious, routine things, which leads the gullible cop Harrison Yates to believe that Cartman is a "child wonderkind" with psychic powers. Cartman is taken to the scene of one of the murders where he has "visions" of ice cream and Double Stuff Oreos (which no doubt have more to do with his own cravings than the actual crime). Yates makes the connection to Tom Johannsen, the owner of the ice-cream store, and he is brutally arrested. Cartman ends up getting more innocent people arrested, including a group of rival "psychics", who threatened to sue him for not using the psychic detective ad and for his refusal to give them 10% of the profits he was making. The left-hand murders continue, including the death of Mrs. Crabtree, but the gullible cops believe these are copycat killings rather than being committed by a single killer (who is seen to be rather eccentric) still on the loose. At every crime scene a disturbed man in a blood-spattered rain slicker named Michael Deets appears. He says to Kyle, Stan and Kenny, "They're never gunna catch the killer, he's too smart." then takes out a female mannequin torso and speaks to it as if it is his sexually abusive mother before walking away. Kyle attempts to draw suspicion towards Deets, but the detectives brush him off.
Kyle knows that Cartman is a fraud, and is frustrated by the police's stupidity. Though he has followed Deets to his home and obtained fingerprint and blood samples, he is completely ignored by the police who regard Kyles 'real evidence' as totally unreliable in the same manner real police are distrusting of supposed psychic detectives. Deciding he has to do something to stop the killer, he imitates Cartman's attempted flight so that he passes into a coma, and when he wakes up claims to have psychic powers and gives the police his original findings. Yates is skeptical but goes to investigate the suspected murderer anyway, who, by this point, has abducted Cartman, furious that the self-proclaimed psychic has credited his work to others.
When Yates arrives, he finds many hands on the killer's wall, but ignores them, claiming that they were right hands. He says that when looking at one's left hand (with the palm facing the viewer), the thumb points to the left. The hands on the wall are nailed with the palms facing the wall, making the thumbs point to the right. Although Cartman is gagged up in the basement, Yates cannot hear him and leaves the house unsatisfied, but he questions his own observation about the hands. He goes back to the station, and after a montage depicting running elaborate criminology tests, exercising, and even losing track of what he was doing, he figures out his mistake, returns to Deets' house, and, he kills Deets, right before Deets attempts to kill Cartman.
Back at the hospital, Mr. Johannsen and the psychics are released from prison, along with Yates and Cartman, and praise Kyle as the real psychic. Kyle then tells them that there are no psychics and says that there is a logical explanation for every psychic story ever heard. Yates says it doesn't really matter now since he stopped the crime using good old fashioned police work. The other "psychics", however, decide to reignite their conflict with Cartman, and engage in a "final battle" (i.e. waving their arms at each other while making silly noises). But just as they begin to gesticulate and vocalize as if acting out a psychic duel, Kyle yells at them to stop, at which point the light bulbs in the room explode and some electronic devices fall off their shelf. Kyle is surprised, but asserts that there must be some logical explanation for this while everyone looks at him with raised eyebrows.