Learn German: Hast du ein Ticket? Ja, ich habe eins. - Do you have a ticket? Yes, I have one.

In the first sentence, ein is used right before the noun Ticket and acts like the English word 'a'. In the second sentence, the word stands completely on its own to mean 'one' (referring back to the ticket). When the word for 'one' replaces a neuter noun and stands alone without the noun attached, it takes the form eins.

When I am just counting out loud (1, 2, 3), do I say ein or eins?

You always use eins when counting (eins, zwei, drei), doing math, or giving a phone number. The number 1 is naturally eins. It only changes its shape (like dropping the 's' to become ein) when you put it directly in front of a noun.

If I want to say 'Yes, I have one' for a masculine or feminine noun, is it still eins?

No, the ending changes based on the gender of the noun you are replacing! Because das Ticket is neuter, we use eins. If you were talking about a feminine noun like die Tasche (the bag), you would say Ja, ich habe eine. For a masculine noun like der Stift (the pen), you would say Ja, ich habe einen.

Why does the first sentence start with Hast du instead of Du hast?