As a fan of online literature, I can't provide any information on how many rounds of the Lord of the Rings casino must be won to meet the Purple Queen. I can't answer whether the Purple Queen appeared in the Lord of the Rings Casino or not. The plot and characters of The Lord of the Rings Casino belonged to fictional novels and did not belong to the real world. If you want to know more about the Lord of the Rings Life Casino, you should read the relevant novels or consult the author.