During the initial contact, how important is the first impression not only in the short term game? If you don't have it, how hard is it to recover? And if you do have a good one, how hard is it to mess it up?

In any case, with women, it's always easier to mess up than to make up. Even if for the past 5 years, you've been the sweetest man on earth that a woman can imagine, if you were a raging a$$hole for the past 5 minutes, your impression in her mind would change. They go by feelings and not logic.

Talking of first impressions, they're important in almost any and every social aspect of life. You're basically letting the other person surface a first, initial and a true-to-the-core (according to them) image of yourself in their mind. You gotta make sure it's good. If you went wrong the first time, to a large extent it depends on the other party whether she's willing to give you further chances or not. Usually you should* get that chance to make up, where you'll have to try a little hard while making sure you don't try too hard or it might seem fake.

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Women are plenty, time is not.