How did the king use the public arena to meet out his own brand of justice?

The king's arena is a symbol of absolute power and of the passions of the soul. The king builds this arena for the purpose of carrying out his unique system of justice that is entirely based on chance. However, the princess corrupts the impartiality of this system when she takes it upon herself to discover what each door is hiding. Thus, it is suggested that impartial justice can never exist and that power corrupts justice in the end.