# Gambler's Ruin in Tennis?

**Discrete Mathematics**Level 4

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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