Be careful with mixers. They can be seen as money laundering by some jurisdictions. Not worth the risk IMO. You might get some privacy, but you could also end up with your account frozen or worse. Most decent sites won’t care about the origin of your coins unless it’s something obviously shady. Privacy is important, but I wouldn't go that route unless you know exactly what you're doing.
Agree with @Moneymaker777. Plus, legit sites shouldn't care about mixed coins. If they do, that's a red flag. Most places want your business and won’t hassle you unless you’re doing something really out of the ordinary. If you're worried about privacy, maybe look into using Monero or other privacy-focused coins, if the site accepts them. Just my two cents.
KYC is a necessary evil these days. Just make sure the site is reputable before sharing your info. And maybe blur out unnecessary details on your docs, like your address or some digits of your ID number. That way, if they ever get hacked, at least your full info isn’t out there. I hate it too, but if you're playing on a decent site, you shouldn’t have to worry too much.
But where's the fun in that? Honestly, though, if you really want to protect your funds, the best move is to keep it all in a hardware wallet and just watch from the sidelines. Less risk, less stress! But if you're going to play, at least do it smartly—set limits, use secure sites, and don’t take unnecessary risks.