Question 130
Ainsley and Buddy play a game where they repeatedly roll a standard fair six-sided die. Ainsley wins if two multiples of $3$ in a row are rolled before a non-multiple of $3$ followed by a multiple of $3$, and Buddy wins otherwise. If the probability that Ainsley wins is $\frac{a}{b}$ for relatively prime positive integers $a$ and $b$, compute $100a + b$.