The major feature for people to grow affinity towards Bitcoin has been anonymity. However, the question to ponder upon would be whether Bitcoin is completely anonymous. At one instance, you should rest assured that Bitcoin is anonymous. However, on the other hand, it may be deemed completely transparent and easily traceable, as every transaction would be recorded in the public ledger.
It would not be wrong to suggest that Bitcoin could be termed as pseudonymous. Receiving and sending Bitcoins would be similar to writing under a fictitious name. In Bitcoin, your fictitious name would be the address in which you would be receiving Bitcoin. In event of your address has been somehow associated with your identity, you would be exposed.
However, as all of monetary transactions on the Bitcoin network would be recorded on Blockchain, people would be able to gather information about the amount of Bitcoins you own on your present address, the address sending you money and the address receiving money from you. In case, you were requesting donations on your website using a specific Bitcoin address, the address would no longer be anonymous.
How can you remain completely anonymous?
Foremost, it would be in your best interest to make use of new Bitcoin address for all transactions conducted by you. It would be a great start despite, it not guaranteeing complete anonymity. The major reason would be you using multiple inputs for transaction and one of these inputs would be coming from the address that has been compromised. It would expose your entire input addresses for bitcoin casino.
Therefore, for improved anonymity, it would be pertinent that you should be using multiple wallets for your Bitcoin Games. By creating a new change address for your inputs, you could be improving anonymity, as the newly created address would only be created, once you get back change from the payments send by you.