Ocean Players Club is the Carnival unit that runs the casinos on all 10 Carnival brands. This is from their FAQ page. (Not in any way meant to dispute the $3000/day thing on Princess, as that may be a recent change, or differs for some other reason).
Q. Can I use my onboard account card to get funds in the casino?
A. Yes, there is no charge at the slot machines for using your onboard account card to access funds. For any transactions completed at a table game, or the cashier’s cage there is a service fee up to 3% each. You can withdraw up to $2,000 per day depending on the cruise line. Please ask the casino staff onboard for further details.
.