"Anything I do throughout this day will yield a successful outcome, no matter what the odds against it are, but only if it's possible to happen in a day."
Let's assume this is literally the rule that has been applied.
For your scenario involving casino gambling, no, you would not be throw out. You wouldn't win much either. A "successful outcome" is not necessarily a bountiful outcome.
Also, time constrained blessings traditionally have backlash worse than their benefit once the time expires. Win a dollar today? Lose three dollars tomorrow.
Me? Spend the day trying not to be too successful.
"Can a casino system prove my (divine) luck as cheating?" -
No, they can't prove cheating due to divinely enhanced intrinsic luck. They can (and probably will) suspect cheating. They can kick you out for no reason (right to refuse service to anyone). But they can't prove cheating.
Slot Machines - Slot machines in casinos these days are typically tied to a central computer system. Machines that show unusual distributions are taken out of service. I think your best bet is ask an employee to pick a machine for you, play thea random machine, win the jackpot (though, see above, re: "successful outcome"), move on to another casino and repeat.