Quote:
"Can I have your number?"
This is a bit low value as you are asking the girl, she can refuse, and it's like you want something from her to make you feel better or give you validation. However, in the right context and with the right tone of voice and frame, it can work. I wouldn't encourage it though.
I would add that this is your average AFC line. Its not one that will destroy any chance you have with the girl, but as you said it will lower your value.
Quote:
"Give me your number"
More commanding and alpha and good to use if you've established an understanding of compliance from her. However if not, this can backfire as she can easily say "No". Again, context is the key and this isn't one I'd encourage, especially for newbies.
Besides context, delivery is also key with this line.
Quote:
"What's the best way to get in contact with you?"
A little bit more low value, but tends to work well in a variety contexts so it's useful as a back up. It's often good to use this if one of the other routes don't work. I was chatting with a girl the other day who honestly didn't actually know her own number (after using the line below). After I said this line, she took out her phone, asked me to put my number in, and then texted me to make sure

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If you use this line at a business party or in a business environment, I don't think it will lower your value at all. As it has a business speak/sound to it. Use it out side of the business environment and I agree it can lower your value. Almost more than "Can I have your number".
Quote:
"What's your number?"
This in my opinion is the best as it's just a straight forward factual question, like "What's your name?" or "What time is it?" It's more likely to get a positive response. If you're into NLP, you'll notice that this has an implicit bind - she can only answer this question by giving you her number! If she can't for some reason, use the line above...!
I also agree its the best general line to use out of the 4 main ones mentioned here.
Quote:
It also helps with the last line to take out your phone while you're saying this, as though you presume that she will give you it (which in most cases she will) which helps with the compliance frame that she is about to give you it.
The same can be applies for "Give me your number" as well.