Bring on the tough stuff - there’s not just one right answer.
Why would Beckett name the play after a stage of a game of chess? How are Hamm and Clov like novice chess players that don't know how to let the game end? Pushing the metaphor a little further, how would an expert chess player deal with the post-apocalyptic world they find themselves in?
Why doesn't Clov leave Hamm? What is it about his cruel master that keeps Clov bound to him? In what small ways is he still defiant?
Imagine that the room that makes up the stage is not actually a room but actually the inside of someone's head, and the two windows in the back are the person's eyes. This makes Hamm and Clov and Nagg and Nell like different characters inside of someone's mind. What parts of our minds might each character represent? Our consciences? Our base desires? Our insecurities?
Why is there so little love in the play? What makes all the characters act so mean toward each other? Where do we still see their vulnerabilities and their compassion?
Why is the play funny? Is it wrong to laugh at people in such a horrible situation? Does laughter create sympathy or does it create distance between the audience and the characters? What is the point of laughing at them?