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I have noticed i struggle with the randoms more so than i do with aquantances. I do not know why.
I think that is because with people you are introduce to, you are more in a comfortable state than with randoms. As you are near someone you know and are comfortable around them so you are comfortable around the girl you where introduce to.
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My goal is to be able to number close randoms, and its not like i am going to approach a girl in the mall and wind up having a 20 minute conversation with her and then get her number.
I actually have done that once.
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I need to do it faster, but don't really know how to do that effectively.
Why do you need to do it faster? I think your first step is to work on getting better at number closing. Once you get better at that then you can work on how fast you can number close. Theres nothing wrong with talking to a random girl at the mall for 20 minutes when there is a conversation going between you and its not forced.