Problem 44503. Anyone for tennis? Your chances of winning a tie-break game

Created by David Verrelli

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Imagine you are playing tennis and the score has reached 'six games all' in a Tie-break Set, so therefore the next game shall be a 'tie-break game', which is now to be played to decide the outcome of this set. For each point played in the tie-break game 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 "tie-break game" of tennis</a> (excerpted below), please determine your likelihood of winning the tie-break 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(0.2125443387076924)</pre>-----" During a tie-break game, points are scored “Zero”, “1”, “2”, “3”, etc. The first player/team to win seven points wins the “Game” and “Set”, provided there is a margin of two points over the opponent(s). If necessary, the tie-break game shall continue until this margin is achieved. "-----See also <a href = "https://www.mathworks.com/matlabcentral/cody/problems/44502">Problem 44502. Anyone for tennis? Your chances of winning a (standard) game</a>.

Imagine you are playing tennis and the score has reached 'six games all' in a Tie-break Set, so therefore the next game shall be a 'tie-break game', which is now to be played to decide the outcome of this set. For _each point_ played in the tie-break game 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 "tie-break game" of tennis> (excerpted below), please determine your likelihood of winning the tie-break 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(0.2125443387076924)

-----

*"* During a tie-break game, points are scored “Zero”, “1”, “2”, “3”, etc. The first player/team to win seven points wins the “Game” and “Set”, provided there is a margin of two points over the opponent(s). If necessary, the tie-break game shall continue until this margin is achieved. *"*

-----

See also <https://www.mathworks.com/matlabcentral/cody/problems/44502 Problem 44502. Anyone for tennis? Your chances of winning a (standard) game>.

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Last Solution submitted on Oct 07, 2021

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Solution 3451468

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Nicolas Schoonbroodt on 28 Oct 2020

Not the cleanest code (I would have used dtmc if the corresponding toolbox was available, and I should definitively improve the code quality itself and vectorize it a little bit)

The problem was fun, thanks :-)

David Verrelli on 28 Jan 2022

I'm glad you enjoyed the problem. You're welcome :-)

I enjoyed looking at your solution too: it had two things I appreciate, namely a creative solution, and ample explanatory comments in the code :-)

Solution 1734799

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Are Mjaavatten on 6 Aug 2021

Kudos for a consistent and elegant approach. Stole the handling of scores > 7 for my second submission.

Solution 1669300

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David Verrelli on 24 Jun 2019

Oleksandr Denysenko, you get no credit for hacking the problem. Only legitimate solutions gain credit.

Solution 1454343

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David Verrelli on 4 Mar 2018

Persistence pays off! :-)

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Problem 44503. Anyone for tennis? Your chances of winning a tie-break game

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