In the US anyway, as the parent said, yes you can deny service for any or no reason except for specific protected classes (e.g. sex, race, religion, etc.). You

In the US anyway, as the parent said, yes you can deny service for any or no reason except for specific protected classes (e.g. sex, race, religion, etc.). You can, for example, deny service to anyone wearing red. Or anyone who is not an adult (or not a child). You can deny service to anyone named Jeeves. There are, of course, edge cases. For example, a shopping mall is a private space but not in and of itself a retailer. IIRC, they are held to a higher standard than retailers and must have a real reason to deny entry. And then there are the cases of using one reason to deny service when really you want to deny service to a protected class. Those are common lawsuit material.