If the first person to win $n$ games wins the match, what is the smallest value of $n$ such that $A$ has a better than $0.8$ chance of winning the match?
For $A$ having a probability of $0.70$, I get smallest $n = 5$ (Meaning there must be $5$ games per match for $A$ to have a $0.8$ chance to win.) I got this by doing $1 - 0.7^5 = 0.832$. Although I would have thought it would have been lower.