Should you a girl a drink? Well, this depends on the situation, but as an opening chat up line, I would say no.
Many girls will talk to you for a while if you are funding their night out. Some girls will take the offered drink and just walk off. If you spend all night buying them drinks, are they into you or your money.
If you nervously go up and ask girls if they want drinks all night, you are going to waste a lot of money.
There are also some women that knowingly go out expecting that guys offering them drinks will be funding their drinking budget for the night. They may even take the offered drink and then proceed to ignore you.
If you are going to buy a girl a drink, it should not be the first thing you ask her. Talking to her for a little bit will give you an idea of whether it is worth your time getting her a drink and whether you really want to talk to her anyway. Importantly, find out if she seems interested in talking to you before offering to buy a drink.
If you are getting desperate, you called always try get some ideas from this great story.
ME: Can I buy you one?
YOU: I already have one, see... (you hold up your drink sarcastically)
ME: Well then, can I reimburse you for the one you are drinking?
YOU: What? (looking at me now)
ME: Let me pay you back for that one."
If the best opening line you have is buying girls a drink, then you need to work harder on your dating skills. Try work on your pick up lines so you have something original that makes you stand out as worthy of the attention you seek.
Don't Take Advantage Of Drunk People
Plying women with alcohol to take advantage of them is also not the best plan. It is also illegal in some places.
There is a gamble buying someone a drink, but it is best to start off a conversation first so you know what you are betting on.