"You bet!" in a reply from restraunt staff to customers saying "thank you" upon leaving.
Hi, everyone!
While I lived in U.S. and went to restaurants there, upon leaving, I would say "thank you" or "I enjoyed a lot” or something like that. Staff would often reply “You bet!” or "You betcha!" I don’t still understand why they say this and its connotation.
I appreciate your input on this.

Question

"You bet!" in a reply from restraunt staff to customers saying "thank you" upon leaving.
Hi, everyone!
While I lived in U.S. and went to restaurants there, upon leaving, I would say "thank you" or "I enjoyed a lot” or something like that. Staff would often reply “You bet!” or "You betcha!" I don’t still understand why they say this and its connotation. 
I appreciate your input on this.

Answer

It's a shortened version of "You can bet on it!" e.g. "You can rely on it!" In other words, they are saying "you are welcome" but in a different way. It's like Preston said, it's equivalent to "absolutely." So, they are saying they have no reservations about serving you.

Answer

Hi, Preston. Thank you for the answer. Based on the answers from you and Miguel, "You bet" sounds to me "Absolutely pleased to serve you" or "You're absolutely welcome". Thank you again.

Answer

It's just an informal way of saying you're welcome or no problem. I don't know how or why the expression came to be. You could also replace it with "absolutely" or "of course" or any other positive response.
-Are you going to the movie tonight?
- You betcha/ absolutely/ of course.
It's just a more enthusiastic response