How do you make bitcoins bought from a exchange anonymous? Contrary to what most people think, bitcoin is not 100% anonymous. It is pseudonym.

Now, let us say you bought bitcoins from a exchange. The exchange has your government issued ID. Then you send your bitcoins to a offline wallet.

Now, the blockchain has a record of the exchange sending you bitcoins to your wallet, and the exchange has a record of what offline wallet is linked to you.

How do you effectively separate this link?

My theory is that you can send your bitcoins from your offline wallet to a bitcoin casino site, then withdraw your balance to another wallet.

Would that remove all the links to your bitcoins from your ID/make it impossible to trace back to you?
You should do some mixing transactions in between, I would recommend Wasabi Wallet or JoinMarket. They are both decentralized solutions, where you don't risk loosing your funds, like it is with centralized tumbling services.