Originally posted on 09/24/2016:
I doubt anyone can explain the exact way they do it. But it would rely on an ever increasing database of information, interrogations of all addresses they run across to try and profile accounts by activity and real world investigation to ID wallet owners.
Remember that even if a book uses a new wallet ID for every transaction at some point they are going to want to consolidate those transactions to either pay winners or cash out themselves. It's not a simple thing to stay anon without a lot of knowledge about how the system works now and what new methods boffins come up with to analyze the blockchain.