Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am not sure I am solving this problem the correct way, as my answer seems too low.

Problem: In squash (a two player racquet game), the player who gets 9 points first wins the game. Whoever wins a rally gets the point, irrespective of who served the ball. I am ignoring other rules for the time being. If player A has the 60% chance of winning a rally, how many rallies, on average, will it take her to win a game?

Simplified problem: I assumed that it takes only 3 points, instead of 9, to win a game. Then I drew a decision tree and assumed that on average X number of rallies are required for player A to win a game. Based on that, I got the following four states, where W = won, L= lost.

W W W – Rallies required to win the game= 3

W W L - Rallies required = X + 1 - 2 = X -1

(subtracting 2, to account for 2 points already won, adding 1, to account for the wasted rally)

W L - Rallies required = X + 1 – 1 = X

L - Rallies required = X + 1

Then I got the following equation.

X = 3 * (0.6)^3 + (X-1) * 0.6^2 * 0.4 + X * 0.6 * 0.4 + (X+1) * 0.4

X = 0.784 X + 0.904

X = 4.19 -The Average number of rallies to win 3 points for Player A.

Is this a correct way of looking at this problem?

Thanks,

MG.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Expected number of rallies to win a game

Loading...

Similar Threads - Expected number rallies | Date |
---|---|

A Value at Risk, Conditional Value at Risk, expected shortfall | Mar 9, 2018 |

Expected number of questions to win a game | Apr 3, 2013 |

Expected number of games in a series that terminates | Oct 31, 2011 |

Computing expected number of particle collisions | Aug 3, 2009 |

Expected Number of Coin Flips | Mar 2, 2008 |

**Physics Forums - The Fusion of Science and Community**