# The probability to win a Tennis match

## How likely is it that the best player is going to win

Last day, I came across a post talking about how a slight percentage of probability of winning a point can get bigger in the probability of winning a match. At first, it seems like magic but thinking about the cascading multiplication of probabilities you can see that it’s logical. So, since I’m a tennis fan, I decided to dig in it and peel back the curtain on what’s behind the scene to know the exact formulas and to figure out the probability to win a Tennis match given the probability of winning a point.

# Problem description

For simplification, let’s consider that in every point you have the same probability of winning and will remain fixed the entire match. We won’t consider fatigue, stamina, injuries, weather, surface type, which side on the court the player is on, serving advantages or psychological pressure due to break points, match points or audience boos.

Let ** p** be the probability of winning any point anytime in the match. If the match consisted of just one point, your…