Why is the seven sided die an appropriate symbol for this story?

Death now introduces the gambling analogy: "It started with gambling. Roll a die by hiding a Jew and this is how you live" (38.7).

(As you can see if you are following along in your book (like you should be!), each section of this chapter begins with a picture of a roll of the die, beginning at one and ending at seven, in order.)

Check out Chapter 38 - The Gamblers (A Seven-Sided Die)