Best guess would be Constantine including it when building up Constantinople, and have it be free, much like the amphitheater in Rome. Market the whole thing as Constantine caring for the public good.
The people were able to go to the circuses, most often for free if I remember correctly. Wasnt if bread and games became free under the Empire? Could we not have to worry about payment and make it a Roman right? Or am I mistaken about the games and how much the Roman infrastructure was provided as a right of being Rome.