In a game show, there is a grand prize of $1 million behind one of three doors. A game contestant picked one of the doors. The show host then open one of the 2 remaining doors that does not contain the prize and ask the contestant if he would like to change his choice (i.e. to stay on his door or to choose the other door that has not been opened). Should the contestant change or stay? Which one has a higher chance of winning?