Luich

Luich is the het ship between Luigi and Princess Peach from the Super Mario fandom.

Canon
As evidenced by Mario and Luigi: Partners in Time and Yoshi's Island DS, Luigi and Peach have known each other since childhood. Both were destined star children kidnapped by Kamek and saved by Yoshi. Back then, they would have play dates.

In their adulthoods, Luigi would occasionally join Mario in saving Princess Peach. However, in game modes such as Super Luigi Galaxy or New Super Luigi, Luigi will save Princess Peach on his own. However, these modes are typically not considered canon due to their purpose of being 'hard mode' versions. Both New Super Luigi and Super Mario Run have Peach reward Luigi with a kiss like any other playable characters.

During the events of Super Princess Peach, Princess Peach saves Luigi. However, she is shown to barely have any regard for him when compared to other games. When rescued, Luigi is referred to as the 'Green Man.' Once Princess Peach saves Mario, she pushes Luigi out of the way, causing the man to faceplant. Though, she calmly walks next to him along with Mario and Perry the Parasol.

Fanon
The ship typically pulls from the multiple hard modes in which Luigi is the protagonist. It acts as a counter to Mareach, in which Mario's younger brother takes his place. Some also believe that Luigi's personality to be more similar to that of Peach's, thus causing them to be more compatible to shippers.

A fairly common trope between shippers who seek a more grimdark version of the ship is that Princess Peach is cheating on Mario. Fan theories even go so far as to state they have even had children together. However, not only are Mario and Peach not officially dating, but Luigi is shown to be loyal to his brother. This belief has began to die down due to rebuttals.

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