Displayed placards stating a business has the right to refuse service to anyone, just how binding is that?

I am sure we have all seen at one time or another, a business that has a placard stating they can refuse service to anyone, but how legally binding is that? If someone comes in with no shirt and but you don’t have a sign stating all patrons must have a shirt, can you not serve him? What if a person comes in reeking of urine, sweat, and beer, do you have to serve him, can you refuse to serve him and ask him to leave? When can you refuse to serve someone and when do you have to serve them no matter what?