It's tough. If someone really had a pile of money out and the server picked up on what they were doing I would approach the table and ask them to explain their thoughts. 9/10 you just gotta let people explain/vent/*****. Whatever the answer would be, I would then tell them it's comes across rude and adds another layer of stress my staff and I don't need. If the person argued with me or said it was his right, I would follow it up with "Well, it's my right to not serve you. Please leave." 99/100 times this shuts them down. If they persisted I would remind them I don't have to serve them as long as I'm not doing it based off of race, sexual orientation, religion, etc. Bascially, we're a private business open to the public and we can choose who we serve to as long as it's not based on any of the above. I would be quick and to the point.
I've asked dozens of people to leave for a multitude of reasons and nearly all involve people drinking. "I remember my first beer" always comes to mind. I tell my managers and our staff "We are ladies and gentleman taking care of ladies and gentleman." As soon as they cross a line, be it volume, curse words or otherwise behavior detrimental to my staff and the surrounding guests, we get serious. We love confrontation and are known as a place that doesn't put up with any bullshit. The local police love us.
When it comes to guests leaving a bad tip, it happens. Servers still have to tipout and I simply remind them this is a part of the business. Don't focus on what you make night-night, focus on your weekly/monthly haul. It all evens out.
