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"This is their right as a private business" -- no, I'm pretty sure gaming is a public accomodation and falls under civil right law. I'm not a lawyer, etc.

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no, you're wrong.

just because you add an IANAL disclaimer at the end doesnt excuse ignorance.

they are a private business and are within their rights to refuse service or bar anyone of their choosing for whatever reason (ie: the same rules that allow casinos to bar card counters)