“Whenever I NEED to sus, it just happens! Si?”
―Amethyst, Steven Poops on the Universe
Ayame Yakumo is the daughter of Yukari Yakumo and Lady Luck. She's a young woman (or at least young by youkai/demon standards) who lives a carefree life in Gensokyo prior to meeting the Mistakes.
Yukari Yakumo is a youkai that doesn't like to sit in one place. She can freely leave the boundaries of Gensokyo whenever she chooses, and she chooses to do that often. Sometimes she comes across interesting people, people who are just as powerful as she is. And that delights her, it fascinates her.
So upon her return from the other world (It might have been Hell, maybe the human world.. Who knows? Lady Luck doesn't sit in one place too long, either), she decided to create something in the image of the demoness she had met. Ran advised against Yukari's idea to create a living being, but Yukari isn't a good listener.
Things turned out well, Yukari managed to materalize a healthy child into existance. The child was mostly raised by Ran and other nearby youkai, since Yukari isn't much of a nurturing type. Ayame does care about her mother regardless.
She's gotten into a lot of Gensokyo magic-related incidents, but that shrine maiden hasn't fought her yet... neither has that witch girl, either. What's a girl got to do to get some recognition?
Ayame wanted to see more of the other worlds, and Yukari didn't want to hold her back, so she allowed Ayame to travel through the border into the world outside of Gensokyo. Ayame decided to take Ryou with her because she felt he needed the experience.
Ayame is very excitable. She's known to often involves herself in things she shouldn't. She figures she should be involved in everything, just like how her mother appears to be. She's eager to prove herself as a powerful and admirable being. She's confident in what she does, even if she does play it up more than she should sometimes.
Ayame is fond of people and she is sociable. She wants to make as many friends as possible.
Like her mother, Ayame has control over gaps and boundaries. However, her power does not extend to, say, life and death or reality and fantasy. Also, her gaps can only lead to places she has already seen.
She, like all youkai in Gensokyo, can use danmaku and spellcards, but she almost never needed to use these abilities. So she's not particularly good at it.
Ayame is also strangely fortunate when it comes to games and gambling. She's also really good at math. She almost always wins.
Yukari Yakumo Edit
Ayame doesn't see her mother as an authority figure at all. Despite Yukari's reputation as a powerful, awe-worthy youkai, Ayame sees her as a youkai that just sleeps all day and has her shikigami do stuff for her. They don't have a bad relationship, but Yukari doesn't really act as a true parental figure. Ran was actually the one to care for Ayame in her early childhood, so she and Ayame are close.
Ayame does think Yukari's powers and reputation are impressive, and she'd like to emulate her in some respects.
Lady Luck Edit
Ayame only knows what Yukari's mentioned about her other "mother." She might like to get to meet the basis of her creation someday, but Ayame's never considered LL to be a mother at all. Which is fine, she's happy with her family in Gensokyo.
Ayame thinks of Ryou as a younger brother. She's visited Eientei and gotten to know his family, and the two have hung out and gotten into many magic-related mishaps. Ayame thinks Ryou is a good kid. Which is true!
Ayame expected Nan to be a lot easier to mess with than he is. In fact, he often seems to be the one causing all the blushing and nervous giggling. How the turn tables!
Ayame thinks that Yuuka is a cool and reliable leader. She'd like to be closer friends with her.