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Questions & Answers about Mam jeden bilet.
Does the number "one" change depending on the gender of the noun?
Yes! The word for "one" acts like an adjective, so it must match the gender of the noun. Because bilet is a masculine noun, we use jeden. For a feminine noun like kawa (coffee), you would use jedna, and for a neuter noun like piwo (beer), it would be jedno.
The verb mam usually requires the Accusative case. Why didn't bilet change its ending?
You are right that mam needs the Accusative case for the thing being had. However, bilet is a masculine inanimate noun (a non-living thing). In Polish, masculine inanimate nouns do not change their endings in the Accusative case. They look exactly the same as their basic dictionary form.
Does the number jeden also have to match the Accusative case here?
Yes, numbers change to match the case of the noun they describe. But just like the noun bilet, the masculine inanimate form of jeden in the Accusative case is exactly the same as its dictionary form. So it stays jeden!
Why is there no word for "I" at the beginning of the sentence?
In Polish, you usually drop subject pronouns like ja (I) because the verb itself tells you who is doing the action. The -m at the end of mam specifically means "I have", so adding ja is unnecessary unless you want to heavily emphasize that I have the ticket.