word order - Why do some questions not start with an auxiliary verb?

When I learned English, my teachers told me that all questions must have an auxiliary verb at the beginning, just like Are you mad? or Is she playing? do.

But when watching some movies or talking with people who speak English, they just ask using things like You mad? and She’s playing?

Of course, the kind of intonation let me know they are asking a question, but why this happen?

Answer

They do start with an auxiliary verb, but since it's predictable, it's often omitted.

These are examples of what's called Conversational Deletion in the literature.
The link has references and further examples.