"King of the Bingo Game" is a doomed story from the start. Although the protagonist momentarily believes that he really can control his destiny, he's ultimately trapped in a "fixed" world. The world is like the movie he watches – no matter how many times he watches sees the movie, it will always play out the same way.
The protagonist has seen this particular movie three times. He knows exactly how it will end. Yet he cannot help wondering what would happen "if a picture got out of hand" (8). This indicates that despite the rigidity of a movie and of a life where "everything is fixed," the protagonist is still hopeful and still willing to dream about free will. We see this dream borne out later when the protagonist refuses to relinquish the button because he dreams of the ability to control his own destiny.