Should a casino manage its own Bitcoin wallet? Let's say I wanted to start an online casino that accepts Bitcoins.

Would it make sense to manage my own Bitcoin wallet for this site? Or would it make sense to just use a third-party service that manages the wallet for me?

What other considerations are there?
Integrating your casino with a 3rd party payments processor translates to much easier bootstrapping for your casino but also higher operating costs. Higher operating costs in turn means that your are by definition less competitive, as you will not be able to provide your users with a smaller over-round and also you won't be able to control the deposit and withdrawal costs. 

Another thing to consider is security; having a 3rd part service deal with your money means that if they fail, you fail; if they vanish, your money vanishes with them.