| I've always given my coat, and had good results. But then again, I am a fan of old school chivalry, so for me that is just basic politeness.
2 tips, though:
a) Wear an expensive coat. The rest of your clothes may be standard (never cheap, but standard), but if your coat is expensive it will help a lot, because the girl will feel the quality, especially the interior linen. If you can, get something tailor made. It's high quality, fits better, and a tag that reads "Made for *your name* by Mr. Something and sons, City X" it's a mark of distinction.
b) Wemen are curious. At any given moment she won't resist to check your pockets. So, "forget" an SPAM recipt there. Check local SPAM's until you find something with a very healthy balance or a generous donation to a worthy cause, like african kids or something. Or anything that will help you look cool or misterious, like a match box with cyrillic writing, a Montblanc pen (or a replica) or something. When I was in college I was invited by a professor to assist to a NATO summit in my town (I was in an intelligence related degree) and they gave me a cool ID card with my photo, name and the NATO logo. If you would read carefully, you woud see "Conference cicle on bla bla, city, 2010" and the word "guest", but at a glance it looks like some high ranking official credentials, and got me some female atention at one time or another.
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