# Gambler's Ruin in Tennis?

Alex and Bob are playing a game of tennis. At any given time, the probability of Alex winning a point is $$\dfrac{3}{5}$$, and thus Bob's chance of winning each point is $$\dfrac{2}{5}$$. If $$p$$ is Alex's probability of winning each Game, find the value of $$p$$ to the nearest thousandth.

Note: In a tennis game, a player wins as soon as he/she has scored at least $$4$$ points AND at least $$2$$ more points than the opponent.. Assume it is possible for the game to continue indefinitely.

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