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1. I was trespassed from a casino that was later sold (like Treasure Island BEFORE they sold to MGM). Am I now allowed to play there since the new owners have never trespassed me?
Your trespass stands only at the original casino. You were trespassed by that business which was sold to another owner. The trespass stands unless you are invited back (which often inadvertantly happens). However your name will still be in the database as undesirable so if you DO go back you should either play under a different name or play anonymously.
2. I was trespassed at an adjoining and similarly owned casino (like Paris/Ballys) am I also barred from Bally's? Legally, the trespass would apply only to the original casino. In this case, however, Paris and Bally's are really one giant casino operating under a single license. Caesars, however, while still owned by the same gaming conglemarate, is incorporated separately, (Desert Palace Inc. d/b/a Caesars Palace) so the trespass legally does not apply (although Caesars may act like it does). Likewise, if you are trespassed at Wendy's Hamburgers on Flamingo, you are still welcome at Wendy's Hamburgers on Tropicana.
3. Being barred at one Stations casino (they all use same players card) does that legally mean all Station casinos? see #2 above, each Station's casino is incorporated as a separate business and then all owned by an overall company. This is done to insulate each individual casino from the others in the event of lawsuits and/or the need to make major changes or even go bankrupt. Therefore a trespass from Sunset Station does not apply to Boulder Station (for example)....however, that won't stop Boulder Station from honoring the trespass at Sunset and re-trespassing you. It also won't keep them from lying to you by saying that you are trespass at all Station Casinos, which they cannot do since the manager at one Station is not a manager for another Station.