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Vegas is good for 3-4 days. Ok, so you're staying up late and sleeping in. That means the casinos will be crowded. If you want to play the drink game, it's gonna be harder. You'll have to look around and know when the cocktail waitress is coming to your area. Otherwise they'll say "Cocktails?" and keep walking. It can be done but the service is slower since they're serving more people.
Ok, so tonight you're going to the pizza place, cool. Buy the booze, bring the food back to your room, and get sloshed. Don't drive the car once you start drinking. Keep the plastic bags from the liquor store and use it as a cooler you can walk with. Yeah, it will drip water so use 2 bags. Put a six pack of beers and ice in there, walk the casinos. Or you can get a beer at the news stand store of each casino, they're usually located near the elevators. It's a tiny store with snack items, wine, and beer. You'll pay less at the liquor store.
If you think you're going to a club, buy the tiny shot bottles to sneak in. Barcardi Limon works good because you can mix it with coke. You can usually fit 2 in each pocket if you're wearing docker pants, and that's 4 drinks.