Winning a tennis game from 30 all

In a game of tennis the points run $0,15,30,40$. A player on $40$ whose opponent has fewer points wins the game by taking the next point. At $40$–$40$ (deuce) the next point gives its winner the advantage; the player with advantage wins the game by also taking the following point, but if they lose it the score returns to deuce.

Novak and Carlos are at $30$–$30$. Novak wins each point with probability $0.6$, independently. What is the probability that Novak wins the game?

$\tfrac{9}{13}$. From $30$–$30$, just like from deuce, a player needs to win two points in a row before the opponent does; a split pair returns the score to a tied state. Novak takes two straight with probability $0.36$ and Carlos with $0.16$, so Novak wins with probability $\tfrac{0.36}{0.36+0.16}=\tfrac{9}{13}$.