You cannot wage 2000 BTC, and be anonymous, the admin of that casino if they are trusted will still ask for clarification and verification, no admin of a casino wants their casino to be an entry point of money laundering, so I don't think no casino will let you wage 2000 BTC or more then be anonymous, you have to look for the side of casinos, they have to answer to the authorities too once they found out that they let people play with a huge amount of money without implementing KYC for verification on the source of funds.
They will put themselves in trouble an eventually authorities will close down or even charge them with conspiracy to launder money.
And that's the simple reason why he won't find one.
It's a lot of money and will definitely be in question how he was able to reach that kind of amount or just simply how he accumulated it.
I would be careful if I have that money.
Tax evasion is the first problem.
Now you are looking for ways to gamble it away which means more questions.
2 BTC should be enough to start in a reputable casino KYC or not. You don't want to be putting your BTC in danger by depositing it with an unknown gambling site.