Santa's Little Helper
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Homer was relying on a Christmas bonus to buy presents, but didn't get it. He was relying on this bonus because the jar of Christmas money that Marge accumulates for the family's Christmas treats was disposed of to pay for the removal of a tattoo that Bart got on his arm. Homer took the small amount of Christmas money he made working as a Santa at the Springfield Mall and bet it at the dog track. He had inside information on what dog was going to win, but instead bet on the "long shot," Santa's Little Helper, believing his name to be a sign. Santa's Little Helper finished last (apparently, it was the latest in a long string of last-place finishes), and his frustrated owner abandoned him. Running to the first person he saw, the greyhound leaped into an angry Homer's arms and kissed him, calming him immediately. Homer and Bart brought him home, and everyone was so happy with him that it was a merry Christmas after all, where he was accepted as the family pet alongside Snowball II.
Sometimes, Santa's Little Helper can be seen chewing on the newspaper and other objects in the Simpson's household (sometimes ignored or tolerated by the family), tearing up the furniture, digging holes in the backyard and eating food from the living room table.
With a few exceptions, Santa's Little Helper doesn't make any sound that resembles a bark. However, he does have an ability to think just like a person. Once, he makes a sound similar to "chewy", and Homer writes it down in his review, unamazed that the dog spoke English. He is also shown to have ridden a circus ball on his hind legs and utter the phrase 'We love... you!' in an attempt to be given some attention from the Simpson family. In addition, he was mascot of Duff Beer, and was known as Suds McDuff (a reference to a similar, real life mascot Spuds MacKenzie).
Santa's Little Helper's life with the Simpsons was not always easy. He nearly died of gastric torsion (referred to in the show as a "twisting of the stomach") because Homer initially couldn't afford $750 for the required operation; and he also broke two legs when Bart's treehouse was demolished by Mr. Burns' slanted oil well drill (The latter of which caused Bart Simpson to hate Mr. Burns immensely).
At one time, Santa's Little Helper was shortly abandoned by Bart for Laddie, a purebred and very well-trained dog he bought from a mail-order catalog together with various other expensive gifts and gadgets. To do that, Bart used a credit card he applied for under the name of his dog, yet the credit card company misread the form and issued a card to Mr. "Santos L. Halper". Laddie learned many tricks that Santa's Little Helper was completely unable to perform (most notably a back flip, CPR and using a toilet). The Simpson family nearly forgot about their old pet, and Bart eventually gave him away instead of Laddie when repo men take back everything he fraudulently purchased. Feeling guilty about this disloyalty and bored with his too perfect new dog, Bart tried to get Santa's Little Helper back. When he finally found him, Santa's Little Helper was serving as a seeing-eye dog for a blind man named Mr. Mitchell, but eventually decided to return to his former owner, Bart.
He also becomes a great hero after he saves Homer in a cornfield maze, and then becomes enrolled as a police dog, teamed up with Officer Lou. Both Lou and Santa's Little Helper make a good team, foiling crimes together. After biting Bart's left leg (due to the fact he got angry when the court stated that he violated one of the police codes while catching Snake Jailbird), Santa's Little Helper is sent off by the Simpson family to live with Lou. Later on, once Springfield Elementary is in danger and Bart isn't able to escape, Santa's Little Helper comes in to save him, and goes back to living with the Simpsons. Unlike when he was the Duff mascot (which depicts the dog as a coward), Santa's Little Helper is depicted as a very brave and smart dog.
Marge and Lisa visited the Springfield Retirement Castle once with Santa's Little Helper. He ran in to the building and played with the seniors. The seniors liked having him there, but a day later when Marge and Lisa returned, the seniors had resorted to watching TV while the dog, now a senior, watched it too. Marge dragged the dog and Lisa, who had turned into a senior almost immediately, out.
Santa's Little Helper has been implied to be bisexual. At the time, the Simpson family is watching a gay pride parade marching down Evergreen Terrace, and one of the groups marching is the Gay Dog Alliance. The marching dogs are clothed in a series of typically camp gay costumes, and Santa's Little Helper, showing excitement by panting, shows an interest in several of the dogs, one of whom winks at him. Santa's Little Helper's attempt to join the dogs is thwarted by the fact that he is currently on a leash, noticing his interest, Homer decides to take the family away from the pride parade.
His kennel was destroyed during the events of Trappuccino, and survived the event by doing things no dog should ever do. Homer then makes Santa's Little Helper participate in an ugly-dog contest, and embarrasses him in front of the town by making him wear an ugly costume. Lisa then tries to cheer him up.
The Simpson family adopted a carrier pigeon once, named Raymond Bird. But, in the back garden one day, Bart let the pigeon out of its cage, where it was eaten by Santa's Little Helper. Bart became resentful of him. Marge and Homer took Bart to see Dr. Thurston, a psychologist, who suggested that he should forgive Santa's Little Helper, as he is the smarter of the two and knows that dogs do not have the brain capacity to know that it is wrong to kill small birds. Bart still cannot forgive Santa's Little Helper, and the family planned to take him to live on a farm upstate, Ostrich World. Bart shared parting words with Santa's Little Helper, telling him never to kill a bird ever again. But, as the family are about to leave, Homer releases an ostrich and it starts attacking the family. Bart calls for Santa's Little Helper to help, but he is confused, since Bart told him earlier it was wrong to hurt birds. Bart ends up clobbering the bird with some nearby tools and forgives Santa's Little Helper. The family then leave, taking the seemingly dead ostrich as meat for dinner.
He sired twenty-five puppies with She's The Fastest once, as well as another litter with Dr. Hibbert's poodle, Rosa Barks.
Santa's Little Helper has been shown to perform abilities that no other dog can. These include standing up on his hind legs and balancing a Duff Beer can on his nose, changing a baby's diaper, and speaking English. He also said (through barks) that he survived Trappuccino by doing things no other dog should ever do.
 Behind the Laughter
Even though Santa's Little Helper's first appearance was in "Simpsons Roasting on an Open Fire", he didn't appear in any other episodes of the first season besides "The Crepes of Wrath". He not appearing in the first seven produced shows was due to the many errors with the animation in the first version of "Some Enchanted Evening".
Once, Marge decided that he needed a bath, but he managed to decipher what Marge said to the rest of the family - "B-A-T-H". He ran riot around the backyard of 742 Evergreen Terrace, and Bart attempted to capture him in a net, but ended up capturing the rest of his family.
After spraining his ankle and finding that Santa's Little Helper has found his way into the Bart Cave, Bart tied a rope around the dog's neck and had the dog pull him on his skateboard, renaming him Bartdog. Bartdog also helped locate criminals with his sniffing abilities. Bartdog also fought Squirrel Girl's squirrels, who were taking over Springfield, with the help of Houseboy, Fighting Owl and Four Eyes.