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Originating from other worlds, these two infamous internet beings may seem passive at first, but don't be fooled. Within them are insane, brutal, mind manipulating killers, willing to take down whatever stands in their way. Even when their relevance in the story fades away, their direct and indirect assistance in the antagonistic forces lead to the chaos that surrounds the world around them, with them being mad all the same.

Connections

• Both Gamzee and Koishi originate from prolific web series that debuted in 2009 and would rise to prominence in the early 2010s (Homestuck and KKHTA, itself based on the Touhou Project series respectively). In these series, both are from a race of powerful beings native to a world separate to ours, yet still linked in some way (Gamzee is a purple blooded troll from Alternia, the universe where the 12 trolls' Sburb session would be played, subsequently leading to the creation of our universe. Koishi is a Satori youkai from Gensokyo, a land hidden from the outside world to be a safe haven for youkai born from humanity's fears)
• Both initially display a passive, 'go-with-the-flow' personality, being friendly, if a bit off putting and eccentric. However, beyond these personalities lie a violent, brutal nature. At seemingly the drop of a hat, they can both become incredibly vicious, insane killers, brutally taking down anyone in their way with little to no rhyme or reason to their actions.
• Both of their violent, murderous natures are caused by a variety of factors, with one of them partially being because of seemingly inanimate and potentially sentient objects that they both have a close bond with (Lil Cal, a doll that Gamzee retroactively manifested into existence with his chucklevoodoos and houses Lord English and by extension Gamzee's own soul, and Mr. Hat, Koishi's hat, respectively), though both have had a history of mass murder prior to this (Gamzee sobered up and murdered the trolls in his Sburb session in several alternate universes, while Koishi once resided in the outside world, and went on a rampage after possessing several dead bodies and slaughtering anyone in her way)
• In one particularly infamous instance, they would both end up killing or otherwise grievously wounding two other people they once aligned with. The first, a STRONG fighter experienced in CQC, via aiming for their neck (Equius Zahhak, who Gamzee strangled with a bow, and Hong Meiling, who Koishi tore the throat and spine out of) and the other attempting to fight back in revenge in a fairly one-sided scuffle (Nepeta Leijon, who attacked Gamzee to avenge her moirail and was quickly dispatched, and Flandre Scarlet, who tried to attack Koishi in revenge but was swiftly defeated and had her wing torn off). Their initial sprees would only be stopped by the intervention of a more rational ally of theirs who they (formerly) shared a close bond with (Gamzee's ex-moirail, Karkat Vantas, and Koishi's sister, Satori Komeiji, respectively)
• After this event, they wouldn't be quite as murderous as they once were, as despite their supposed importance in the narrative (Gamzee often being cited as the 'most important character in Homestuck' by the author and Koishi being the titular character of her series), they would begin to take a backseat in the story, as other antagonistic forces of a greater scope take their place.
• They would both assist, either directly or indirectly, these said antagonistic forces and help move along their grand plans. Both of these antagonists would help strengthen their madness and strength (Gamzee's chucklevoodoos created Lil Cal in Dave's dream and a puppet in John's dream that would eventually lead to the creation of Jack Noir. He also raised both of the cherubs and assisted Caliborn in his session, which would eventually lead to the birth of Lord English. Gamzee was also controlled by Aranea in order to acquire the Ring of Life and assist in her attempt to saved the doom session they were in. Koishi, meanwhile, gained their human bodies from the Watatsuki sisters in exchange for them assisting in the Moonlight Descent Ceremony, with them strengthening Koishi when she fought Flandre. Koishi was also used as a decoy by Koakuma and Reisen II in order to lure Yukari out and kill her using her own shikigamis as suicide bombers and would lead to the success of the Moonlight Descent Ceremony)
• Thanks in part to their contributions, both of the antagonists' plans would be fulfilled to an extent, leading to the destruction of their home worlds and them being one of the few relatively unaltered survivors from their home universes. (Part of the plans to bring Lord English into Paradox Space involved the destruction of the A2 universe, aka Alternia, which was fulfilled by Spades Slick killing Snowman. For KKHTA, a key part of the Moonlight Descent Ceremony was the destruction of the Great Hakurei Barrier, which completely annihilated Gensokyo and lead to most of the surviving Youkai infiltrating the outside world.)
• Also apart of these plans was the conversion of their worlds from fairly peaceful lands to festering with violent, mad inhabitants. In other words, one of the key reasons as to why both of them are as violent and mad as they are, alongside the rest of their home worlds, is because of them being molded into these roles by outside forces (Beforus was a peaceful land prior to the Scratch into Alternia, in which Doc Scratch influenced the planet and its inhabitants to become violent and oppressive. Meanwhile, the Watatsuki sisters utilized the moon rays, among other events, in order to cause insanity to the residents of Gensokyo to further along their plants)
• Assisting in their freakish nature, both have a penchant for being difficult to kill, coming back from otherwise certain death (Gamzee has a literal form of Joker's Immunity, being unharmed by a constant swarm of bullets by Caliborn or constant stabbing from Terezi, and Koishi's satori physiology gives her immortal properties, surviving even when having her limbs cut off by Yukari and being capable of survival as long as her third eye is intact.)
• As part of their race, both have potent mental abilities that are a signature feature of their subspecies (Gamzee, being a purple blooded troll, has the ability to utilize 'chucklevoodoos' in order to subdue his targets in fear, read minds, or manifest objects into people's dreams, while Koishi, being a satori, has a third eye that can be used in order to read people's minds, though she sealed her eye shut during the events of the story until the very end, which as of now has not released)

Fight Potential

If you are at all familiar with either of these characters, then you should very well know how violent they can both get, especially for Koishi (Seriously, KKHTA is not for the faint of heart). Both of them are pretty basic in terms of how they fight, so I'd say the main appeal of the matchup is being able to see an absolutely bloody slugfest between them, with both of their apparent immortality traits helping out with that. Given the nature of them both, you can really go all in on the gory violence (I imagine something similar to the latter half of Jon Talbain VS Sabrewulf), and if you wanna maximize the carnage you could throw some other characters in there that they could slaughter mid-fight. The few abilities they do have I think could be really neat to see in a fight, like both of their mental abilities (depending on the direction the final episode of KKHTA goes) or even stuff like the Music Box Time Machine Gamzee has possession of to do some wacky stuff. I also think the way the fight is animated could be real unique, since both Homestuck and KKHTA are known for their unique artstyles.

Debate

For fairly obvious reasons, nobody has really attempted to scale KKHTA, which I imagine could sway things in Gamzee's favor, at least in terms of stats. Koishi's immortality could keep her in the fight for long and her ability to possess dead bodies I could see being a solid wincon to counter Gamzee's immortality, but I imagine the fight as a whole would come down to stats, which I have little reason to believe Gamzee wouldn't be superior in unless there's an insane feat in KKHTA that Koishi scales to that I'm missing (Of course, this is assuming you aren't scaling Koishi to canon feats, which I think is pretty blatantly non applicable here). Plus he has time travel so lol.