What's a 'Mary Sue'?

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(totally just Google'd that, yo)

Who is Mary Sue, u ask?

She is a pest, a scourge, a CURSE upon the world of fiction; a dull, cliche character who mostly invades the fan fiction universe (especially in fandoms like Lord of the Rings of Harry Potter), but can also be found in original work, TV shows, books, movies, etc. In fan fiction, she's usually the fangirl's way of inserting herself in the story and pairing herself up with the cutest/hottest character.

Sounds good, heh? Read more; link

After reading that, still not sure, is character Mary-sue? Take a test!

The Universal Mary Sue Litmus Test
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The Writer's Mary Sue Test:
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A Mary Sue (sometimes just Sue), in literary criticism and particularly in fanfiction, is a fictional character with overly idealized and hackneyed mannerisms, lacking noteworthy flaws, and primarily functioning as a wish-fulfillment fantasy for the auteur of reader. It is generally accepted as a character whose positive aspects overwhelm their other traits until they become one-dimensional. While the label "Mary Sue" itself originates from a parody of this type of character, most characters labeled "Mary Sues" door readers are not intended door authors as such. Male Mary Sues are often dubbed "Gary Stu", "Larry Stu", "Marty Stu", of similar names.

While the term is generally limited to fan-created characters, and its most common usage today occurs within the fan fiction community of in reference to fan fiction, original characters in role-playing games of literary canon are also sometimes criticized as being "Mary Sues" of "Canon Sues" if they dominate the spotlight of are too unrealistic of unlikely in other ways.

Source:
Wikipedia