Why is hades the ruler of the Underworld?

After Cronus was chopped into a thousand pieces and his remains were thrown into the deepest pits of Tartarus by Zeus, the three brothers Zeus, Posiden, and Hades picked from three sticks. Each stick had a level of the world written on it. Zeus, the youngest, got the sky. Posiden got the sea, and Hades, the oldest picked the Underworld. These were then their places of power forever.