It's not private anymore if a casino will require us to comply with the KYC.
Though there are still a lot of casinos that really offer anonymous gambling, the moment they get a license, it's just like they are turning into a fiat casino because they are already regulated, hence gamblers have to comply with the regulation.
It's only private if it's a "real decentralized" system that we are using, unfortunately, it does not work that way becuase bitcoin is only a payment method and we still follow the typical type of gambling.
KYC is the standard. Apart if this is good, I avoid small casino's etc. Had a bad experience in the past hence i i only gamble, for fun, with the big boys.
Just make sure to follow the book when you win, governments are not too fond of crypto, nor will they of you when you try to bypass the law.. And yes casino's have to cooperate...