I was up $800 in Vegas Counting Cards at Blackjack and they threw me out, can i file a lawsuit?

I would look into Nevada state gambling laws to see if counting cards is illegal or not. If it is then filing a lawsuit will just put you in jail. If it's not then yes you can file a lawsuit for all the money they owe you plus court costs if they did not give you your winnings before throwing you out. If they gave you all of your winnings then you cannot sue because it is private property and they don't have to let anyone in that they don't want to. Just like you can't be sued for kicking someone out of your house.