Consider three custom dice:

• Die $A$ has faces $\{2, 2, 4, 4, 9, 9\}$.
• Die $B$ has faces $\{1, 1, 6, 6, 8, 8\}$.
• Die $C$ has faces $\{3, 3, 5, 5, 7, 7\}$.

A player rolls Die $A$ and Die $B$. What is the probability that the roll of Die $A$ is strictly greater than the roll of Die $B$?