What's the deal with licking the cigarette?

It might make the cigarette burn slower. Not sure if this is a cultural thing or not as I haven't noticed a lot of Americans do this.

I found it funny however when Edo was so stressed out that he licked his cigarette and then lit the filtered end.

The only reason I could give for licking the cigarette is that maybe they are licking the seam of the cigarette to keep it from splitting? Perhaps the cigarettes are cheap and they are afraid they will fall apart at the seam?

Allegorically, it ties her to her father--daddy's girl--who openly approved of her smoking (in contrast to the estranged and disapproving bitch-mother). At first I thought it might be a regional thing, that tied her to her small town (Krko), but when she went back there (several times), no else there did it, just her dad, who obviously raised her.

Why did dad do it? Well, it was made clear he was a drug-using rocker during his misspent youth--lead singer no less--so I'm guessing he used to roll his own joints, licking the length of those rolling papers... to the point where he didn't even think about it any more. Kinda like if you've always owned/driven stick-shift vehicles, and then you borrow/rent one with an automatic, your left foot still wants to do a little clutch work, lol.

Anyway, the deliberate, coordinated manner in which the daughter did it was much more stylish--and usually much more LEWD (I APPROVE! ;')--than the sort of absent-minded way the dad did it. Her character might've even considered it a signature aspect of her persona.

I don't think it has anything to do with slowing the burn, or mellowing the smoke. It might have to do with making the promo-trailers more intriguing, lol.

It's mostly done when you rolled your own cigarette too kep it toghther.

as already pointed out,it ties here to her father. It is a meme and one quite popular in Europe. I am sure there is a reason for it.

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Life's too short for mediocrity.

Many smokers have their special rituals for smoking. I have never seen the cigarette licking thing, but I know some smokers like to tap their cigarette three times before they light it. The tapping supposedly jolts the tobacco inside the cigarette, which makes it better for some reason.