Still on the case, if the punishment of accounts blocking is the price that ignoramus and stubborn gamblers has to pay, what does the casino do with such money after then? Do they convert the money for themselves or they have an authority they pay such money to?
Gambling establishment are businesses. As such, every business is aimed in making and maximizing profits as much as possible.
Before a potential customer gambles in a given online gambling platform, they are presented with the TOS of the gambling website. Included in the TOS are the said violations and consequences that a potential customer may experience in the event of any kind of infringement. In the event that a customer violates a certain provision in the TOS, the funds inside their accounts would be confiscated and it will invested back into their gambling system.
Like some persons already said, if a casino block customers account for any reason that is related to money laundering and if after blocking the account, the person still has some money in that account, the casino will give the money to the government authority that is in charge of money laundering but if the money is not connected with laundering, they will claim the money because the customer no longer have access to it again.
This really depends on the TOS and the type of violation a gambler infringes.
Like what you mentioned, if the violation is due to money laundering, then the money would be confiscated and surrendered to the custody of the government. For any other violations not involving a federal crime but a violation of their TOS (e.g. creating multiple accounts, ban evasion, etc.) the funds would be re-invested back into the business for their benefit.