What does the Casablanca quote "here's looking at you, kid" mean?

Question

I'll begin with saying English isn't my native language and this sentence doesn't make any sense to me.

How's that grammatically correct?

The expression "here is" is usually followed by the name of a place/person as in "hey, here's Marco Polo, he's back with tales of adventures".

"What/who" is here looking at her? It sounds like some words are missing, like the subject.

Could someone please rephrase that sentence keeping its original meaning? Thanks!

Answer 1

"here's looking at you" is an American expression

It is a play on the card game of poker, when the face cards (JQK) are all looking at you: good news if you hold them

so when I lay my cards down and say this, well you have lost the hand

Answer 2

It's not supposed to be grammatically correct.  In the movie Casablanca, Bogart toasts Bergman, and he uses that line, "Here's looking at you, kid."  When you give a toast you usually say, "Here's to Marco Polo for having adventures."  In the movie though, Bogart is trying to illustrate that he loves looking at Bergman so that's why he says it.  Bogart played a lot of gangsters in his movies, so he didn't always speak correctly.  It doesn't take away from the beauty of the line, rather it makes it more poignant.