How can Percy and his friends play all the games in the Lotus Hotel casino, when they are still teenagers and the legal age to gamble in Las Vegas is 21?
I think what is really going on is that anyone going into the casino would be put under the spell of the lotus flower (assuming consumption) and after that just doesn't care. The "proprietors" of the casino don't care. Their whole purpose is to draw people in and keep them there. Any "authority" who would normally be keeping this sort of thing from happening would more than likely get drawn in by the flower as well, so too, wouldn't care. It's not illegal for a minor to go into a casino. It is only illegal for them to play the games. If nobody is looking or caring who is playing the games, let it ride.