What should I do with a girl who plays hard to get?

TigerRoseBear
Please answer :)

So I like this girl, and I know that she likes me back (I know she likes me, but she doesn't know that I know). I think she probably guesses that I like her too, based on the fact that I sent her an email yesterday, even though she never gave me her email address, and the only way I knew her email was I saw her email address in a group email sent out to like 20 people, and the group email was from the end of August. And I emailed her because I heard she was sick, and I pretty much just told her get well, and congratulations on doing well in a squash tournament this past weekend. I emailed her because she didn't show up to squash training yesterday (we train together), and that's when I heard from two people that she was really sick. So she never ended up replying to the email. Then today, she showed up to training, and I asked her, "Oh, you got better?" and she said that she was never sick (?), but just went to see her school basketball game yesterday, and her brother (13 years old) played along at first but after around five minutes said to me that she was sick, but even after I asked her "then why did your brother say you were sick?" she still said she wasn't sick. I don't know, maybe she just has a really weird sense of humor - for example, she told me a couple weeks before her birthday when exactly her birthday was, and a couple of days before her birthday, I went up to her and said, "hey, your birthday's coming up, right?" and she said "no, it was last Saturday", even though it was the coming Saturday. Then, on her birthday (Saturday), she told everyone it was her birthday.

Anyways, it just seems like she plays hard to get a lot of the time even though I know for sure she likes me. And one time, I saw her trying to make me jealous - she talked to a boy for about a minute in plain view of me (like, they were right in front of me about 10 meters away, and I was on a spin bike, so I was directly facing them), and after he left, she looked at me to see if I was looking at her, but I pretended I was looking at something beside her, and she saw that I was looking at something else, and so she looked at what I was looking at for around 2 seconds then carried on doing what she was doing.

Pretty much, again, I think she plays hard to get a lot even though she likes me. What should I do with someone like that? Do girls who play hard to get want to be chased, and is it a good idea to chase them, and really try to show them that you like them, or is it better to play hard to get as well (in moderation of course)?
Updates:
+1 y
I know some of you think that her not replying to the e-mails means she doesn't like me, but I know for sure she likes me...

If you want to know how I know, read the description / updates of this: (see next update)
+1 y
+1 y
Another thing: A lot of you seem to think that any girl who plays games is a bitch. I don't really know this girl well enough to know if she's a bitch or not - if I get to know the real her, I could find that she's a really nice girl. But anyway, to...
+1 y
the people who think she's a bitch: I'm pretty sure that often, girls play games (e.g. hard to get) because they just want their crush to like them back, not because they're mean or manipulative. So I would like to get to know this girl, instead of...
+1 y
just labeling her a "bitch" and not wanting anything to do with her.
+1 y
I think that ignoring her back seems to work (today I ignored her at training, and she ignored me, but then she sat in front of the court I was playing on watching me for about five minutes - which is actually a long time), but what should I do after? I..
+1 y
think I do want to ask her out sometime, but I'm not sure how to, or where we would go (maybe the movies, what do you think).
+1 y
Thanks for answering, everyone! So, I feel pretty stupid now lol, because I thought she liked me, but it turns out she doesn't - I asked her two days ago if she wanted to see a movie with me sometime, and she just smiled, said she was really busy, and
+1 y
walked away. Here's what happened today: link
What should I do with a girl who plays hard to get?
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