I just met this girl a month ago and I really like her. No idea if she likes me, although there are a couple signs, but I'm ready to work at it.

I found out from a friend of hers that her previous relationship ended only 5 months ago and that the ending was mutual. Her boyfriend got transferred to another city and they weren't at that stage where she was like ok i'll pick and go too, so the relationship ended because it had to, not because they didn't like each other. They also said no to LDR. And even though it was mutual, it was her who said this has to end.

I haven't asked her out yet, and I'm pretty sure she'll say no if I do because after a month I can say the following:
(1) Even though he's officially an ex, there's still strings attached. I think she's ready to move on, but im not 100% sure yet. And I can't see how SMT would work here because she obviously still 'likes' him.
(2) If I ask her out she'd say something like.. I don't know that much about you, let's just stay friends. I mean in my POV going out/dating is all about getting to know more about someone so either she's just trying to be nice by not explicitly saying no or she likes to become friends to get to know someone then stepping it up. I could be reading too much into it.

Anyways... how do you game a girl like that? A girl who is still 'attached' to her ex and also needs to trust and know you before going out with you.

When I put it like that I guess I answered my own question - just be her friend. That won't work because she already has friends and one in particular (a guy) who she trusts like completely. The way they act basically makes it look like they are bf/gf... they do everything except have sex and kiss - that's how close their relationship is. And before you think this guy is gay, he isn't. He asked her out - twice - and both times she said LJBF.

To me it seems like she is still attached/loyal/isn't ready to move on from her ex, but still wants that emotional contact/bond which she can get from that aforementioned guy friend. And I need to break through that. But how?

Your not just her friend, and don't ever become that; take her to a park, or some mall (if your that strong lol) somewhere to hang out casually. You can build major rapport and DHV doin this (Get her number first if you havn't). The guy friend she "trusts completely" is more of a excuse for you not to try, if he's been LJBF he's not a problem and she wouln't blow you off for him; he really is just a friend if she trusts him that much.

Also if she's not over him now, she never will be. Game her like her ex never existed and you'll either score or figure out she's to into her ex to much to ever move on. Never play the "I'll wait until your ready and moved on" game with women, they win everytime.

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To game at your best you have to be willing to do your worst.