Problem 44502. Anyone for tennis? Your chances of winning a (standard) game

Created by David Verrelli

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Imagine you are playing tennis, and for each point played your chance of winning is <tt>x</tt> % (input as a <tt><a href = "https://au.mathworks.com/help/matlab/ref/uint8.html">uint8</a></tt>). Given the <a href = "http://www.itftennis.com/procircuit/about-pro-circuit/rules-regulations.aspx">ITF's scoring system for a "standard game" of tennis</a> (excerpted below), please determine your likelihood of winning a game (output as a <tt><a href = "https://au.mathworks.com/help/matlab/ref/single.html">single</a></tt>).Note that as <tt>x</tt> is taken to be the same for every point in this problem, it does not matter whether you are serving or not.EXAMPLE<pre> x = uint8(40)
 chance = single(0.2642707692307693)</pre>-----" A standard game is scored as follows with the server’s score being called first:<ul><li>No point - “Love”</li><li>First point - “15”</li><li>Second point - “30”</li><li>Third point - “40”</li><li>Fourth point - “Game”</li></ul>except that if each player/team has won three points, the score is “Deuce”.
After “Deuce”, the score is “Advantage” for the player/team who wins the next point. If that same player/team also wins the next point, that player/team wins the “Game”; if the opposing player/team wins the next point, the score is again “Deuce”. A player/team needs to win two consecutive points immediately after “Deuce” to win the “Game”. "-----See also <a href = "https://www.mathworks.com/matlabcentral/cody/problems/44503">Problem 44503. Anyone for tennis? Your chances of winning a tie-break game</a>.

Imagine you are playing tennis, and for _each point_ played your chance of winning is |x| % (input as a |<https://au.mathworks.com/help/matlab/ref/uint8.html uint8>|). Given the <http://www.itftennis.com/procircuit/about-pro-circuit/rules-regulations.aspx ITF's scoring system for a "standard game" of tennis> (excerpted below), please determine your likelihood of winning a game (output as a |<https://au.mathworks.com/help/matlab/ref/single.html single>|).

Note that as |x| is taken to be the same for every point in this problem, it does not matter whether you are serving or not.

EXAMPLE

x = uint8(40)
 chance = single(0.2642707692307693)

-----

*"* A standard game is scored as follows with the server’s score being called first:

* No point - “Love”
* First point - “15”
* Second point - “30”
* Third point - “40”
* Fourth point - “Game”

except that if each player/team has won three points, the score is “Deuce”.
After “Deuce”, the score is “Advantage” for the player/team who wins the next point. If that same player/team also wins the next point, that player/team wins the “Game”; if the opposing player/team wins the next point, the score is again “Deuce”. A player/team needs to win two consecutive points immediately after “Deuce” to win the “Game”. *"*

-----

See also <https://www.mathworks.com/matlabcentral/cody/problems/44503 Problem 44503. Anyone for tennis? Your chances of winning a tie-break game>.

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