3. Deposit BTC into a centralized gambling site or exchange and then withdraw your funds.
In case of going with the 3rd option, you should know that these services will know so it's not as secure/safe as the first two options.
I thought you were worried overly! At these sites, they process millions of transactions every day, which means they won't have enough time to check what you're doing with your money. However, if you follow this way, you will incur a cost of 2 times what you have to pay, it's too costly to make. So choose the first one.
I don't think OmegaStarScream is paranoid when saying it's not as safe as the first two... Afterall, if i'm mixing my coins, i'm not worried about an exchange analysing all of it's transactions, instead i'm worried about a foreign governement or a hacker singeling me out, searching for my transactions in particular.
When using an exchange, their internal records will show my ip(s), my browser fingerprint, timeframes when i was active and a link between deposit addresses, currency exchanges and withdrawal addresses. Imagine what a 3 letter agency could do with a dump of their database when they are trying to track me down. Even worse: imagine what a malicious hacker could do if he managed to get his hands on the exchange's database and tried to track me down for extortion or robbery.
Personally, i'm a big fan of mixing services. However, you do have to realise these services are anonymous themselfs. You have no guarantee the mixing service itself isn't a honeypot. Personally, i use mixing services to hide my transactions for malicious individuals and to protect my privacy, so i wouldn't care to much if one of the mixers i use turns out to be a governement honeypot. However, i guess some people might be in problems if their mixer turned out to be ran by a 3 letter agency.