The sophisticated woman usually is sophisticated for one of two reasons. She is either sophisticated because it was her whole family upbringing and cultural orientation, or she is sophisticated because she was once insecure (not knowing where she belonged). She then tried for what she considered the highest strata, and made it.

If she is the first, the only way to ever win her is to have been brought up in the same kind of atmosphere as she has, or to have become so popular (great author, school president, leading athlete, etc.) that you consider yourself her social equal. Technique or style just won't do it.

There is a saying that goes, never marry the woman you would marry if you were a better man; you will hate her for her superiority in trying to make you into an equal.

For the other kind of sophisticated woman, give her lots of compliments and occasionally call her bluff. There will be no end of interesting dialogue. Though you may win her, you might not know what to do with her.