Interesting and complicated topic
Indian casinos and the tribal courts have no criminal jurisdiction over non-Indians so it is unlikely you will be sent to an Indian jail. Tribes are not independent nations. The standard definition by the courts going back 180 years is that the Indian nations are "domestic dependent nations".
If you break a state or federal law while on tribal territory you could be turned over to the appropriate authorities. There are no laws in the US against counting. As much as the casinos might desire such laws there are a few possible constitutional problems with banning people from thinking. You can, of course, be tossed out. In reality, the tribal casinos, like the private casinos in all but a few jurisdictions, can exclude anyone they want. Tribal authorities can also pretty much exclude any non-Indian from tribal territories.