Note: while Patrick Roach appeared in the original Trailer Park Boys movie of 1998, he was not playing Randy, but instead playing a different character also called Patrick.
Randy lives with Jim Lahey most of the time, in the supervisor's trailer. On those rare occasions when he has been not been with Jim, as the result of a break up or other extraneous circumstance, he tends to gravitate toward going back to the streets as Smokey the male prostitute ("A Man's Gotta Eat"). However, in the beginning of season two, he is found living in Lucy's trailer and says they are in love ("What In The Fuck Happened To Our Trailer Park?").
When Jim was ousted as the park supervisor, him and Randy lived in the supervisor's car on a vacant lot in the park, until Ricky took that away from them too ("Never Cry Shitwolf").
Randy has lived in the supervisor's trailer alone, on the occasion that he was the Associate Park Supervisor in season six ("The Cheeseburger Picnic").
Randy's sexual orientation is clearly bisexual, since he enjoys a relationship with Jim Lahey most of the time, but also expresses and shows interest in romantic interest in both Lucy ("What In The Fuck Happened To Our Trailer Park?") and Sarah ("Never Cry Shitwolf") during the series. He occasionally becomes confused by his feelings on this, even seeking the advice of Bubbles in one episode, who then told him him that there was nothing wrong with being attracted to 'whatever' ("Halloween 1977").
Whenever possible, Randy is with Jim, because they are clearly in love with each other, but there are many breakups and arguments throughout the show, as both characters attempt to deal with their feelings and issues with each other, their affections for other people entirely and attraction to both genders in general.
In season two, as mentioned before, Randy lived with Lucy, but that arrangement seemed to be more of a subjugating position for Randy as he was ending up doing most of the chores around the house. It did not last.
Randy briefly experiences arousal by Sarah, and decides to tell her about it, but she is not interested and just wants to be friends ("Halloween 1977"). Nothing more is said about this.
In season six, Randy breaks up with Jim because of his alcoholism, and shortly thereafter takes up with Officer Ted Johnson ("The Cheeseburger Picnic"). Ted, Like Lucy, ends up trying to change him, forcing him to wear shirts, and bossing him around, and Randy doesn't take kindly to this either, and the relationship ends ("Halloween 1977").
Season seven sees Randy with Lucy again, after they fell in together while Ricky was in the drunk tank. Their tryst results in a baby (Ricky assumed it was his) which the two of them attempt to raise together ("I Banged Lucy And Knocked Her Up... No Big Deal"). However, it seems fraught with problems, mainly the fact that Randy is high all the time, and seems to have no interest in much else. Eventually, he once again goes back to Mr. Lahey at the end of the series ("Let The Liquor Do The Thinking"). But in "Countdown To Liquor Day", Randy and Lahey argue more aggressively than they ever had before, and break up, which sends Lahey over the edge, especially when Randy plays on Jim`s innermost desires by saying he is now living with Julian, knowing full well that Jim has an ongoing crush on him.
Randy doesn't generally break the law, unless its in collusion with Jim or someone else. Apart from his prostitution outings as Smokey and occasional to chronic drug use, Randy remains fairly law-abiding and has mainly only been jailed as a result of his association with Jim. There are many instances both on screen and off where they have spent the night in the 'drunk tank'. Other minor crimes include breaking & entering and petty theft (to steal evidence to get the boys arrested in season six. Randy has also been charged with drunk driving on one account("Gimme My Fuckin' Money Or Randy's Dead")).
Randy does not wear shirts unless he absolutely has to. He almost always appears topless, and wearing a pair of tight white pants and a belt. This accentuates his ample gut and it's a source of humour and taunting in the park. If he is about to get in a fight, he always removes his pants because they are too tight to maneuver in, and he doesn't want to rip them. Basically, Randy has an unusual attachment to his pants. In some episodes characters such as Bubbles (who tried to force a shirt on Randy after he refused to put on a shirt that Alex Lifeson asked him to put on backstage at a Rush concert) and Ricky attempt to get Randy to wear a shirt but both times he takes them off. In one other episode Randy wears a shirt bought by Lahey's daughter Treena (she originally bought the shirt for Ricky after pawning her bike to Cory and Trevor, and in the end Treena gave it to Ricky) when attempting to make Ricky, Julian, and Bubbles think he wanted to be friends, but he really just wanted to get close and spy on the boys for Mr. Lahey. It was revealed he was using the shirt to cover up his walkie talkie that he used to communicate with Lahey. Later on when he was involved with officer Ted Johnson he was asked to wear a blue police t-shirt by Ted and he agreed to wear it.
Randy is addicted to cheeseburgers, another source of humour. He needs them like a junkie needs a fix, and it's an issue between him and Jim on several occasions. Randy always makes sure he has plenty of burgers on hand at all times, and doesn't like it when people get into his stash. Cheeseburgers is a motivational tool for other people to get Randy to do their bidding; Ricky bribes him with cheeseburgers in trade for working on building a dope trailer, Lahey gives him a burger made out of dead blue jay to get him back.
One gets the impression Randy has always been the kid that always wanted to be one of the guys, but no one liked him and sent him away as the lone outcast in any group. So because of this, Randy is easily influenced, and will go along with just about anyone if it seems that they want to spend time with him for any reason.
Randy seems prone to drastic changes in demeanour. Sometimes he is seen as a timid shy person who speaks softly, very much the subjugate, but at other times he is aggressive and violent. Many people in the park are quick to say that when Randy is provoked you need to watch out, because he will take his pants off and destroy you. In fact, he instigates fights on a few occasions, with Ricky, J-Roc, Ray and is instrumental in removing Cyrus from the park in season four through means of a fist fight. He stands up to Jim many times, but at other times, he seems too willing to just do Jim's bidding.
Real World Perspective: Randy's Timeline Anomaly Edit
In the Christmas special "Dear Santa Claus, Go Fuck Yourself", which is set prior to any other episode or movie, Randy is caught working as a male prostitute by Barb Lahey in December of 1997. When she takes Randy home to help him, both Randy and Jim Lahey are surpriesd and it is implied that Lahey has been paying for sex with Randy. From this it can be surmised that Randy was not assistant supervisor under Jim until at least this date.
In the first episode of the series, "Take Your Little Gun And Get Out Of My Trailer Park", when Ricky arrives back in the park after being released from jail, he questions Randy, "What are you, his(Mr. Lahey's) new assistant?" To which Randy replies, "Yes I am." It is clear from Ricky's reaction that Randy must have become assistant supervisor while Ricky and Julian were in jail (unknown sentence length).
Later in "Jim Lahey Is A Drunk Bastard" Randy states that he has been the assistant supervisor for 12 years without a promotion, and this episode first aired in 2002 (It is unknown what year it was supposed to have taken place in the TPB universe).
In order for this statement to make sense with the other two pieces of information, Randy would had to have been either fired, quit or otherwise discharged from his job before Ricky went to jail prior to the events of "Take Your Little Gun And Get Out Of My Trailer Park". This is the only way that Ricky could reasonably express surprise upon hearing the news of Randy's "new" position. This is a contradiction of Randy's assertion that he has been the assistant supervisor for twelve years.
However, "Dear Santa Claus, Go Fuck Yourself" is the only episode of the entire series for which the date of occurrence is known for sure. Given this fact the above timeline could be completely correct, and any suppositions to the contrary based on episode air date are largely Ignoratio elenchi.