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

Created by David Verrelli

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>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</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>each point</w:t></w:r><w:r><w:t> played in the tie-break game your chance of winning is</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>x</w:t></w:r><w:r><w:t> % (input as a</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t></w:t></w:r><w:hyperlink w:docLocation=\"https://au.mathworks.com/help/matlab/ref/uint8.html\"><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>uint8</w:t></w:r></w:hyperlink><w:r><w:t>). Given the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.itftennis.com/procircuit/about-pro-circuit/rules-regulations.aspx\"><w:r><w:t>ITF's scoring system for a \"tie-break game\" of tennis</w:t></w:r></w:hyperlink><w:r><w:t> (excerpted below), please determine your likelihood of winning the tie-break game (output as a</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t></w:t></w:r><w:hyperlink w:docLocation=\"https://au.mathworks.com/help/matlab/ref/single.html\"><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>single</w:t></w:r></w:hyperlink><w:r><w:t>).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Note that as</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>x</w:t></w:r><w:r><w:t> is taken to be the same for every point in this problem, it does not matter whether you are serving or not.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>EXAMPLE</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[ x = uint8(40)\n chance = single(0.2125443387076924)]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>-----</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>\"</w:t></w:r><w:r><w:t> 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.</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>\"</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>-----</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>See also</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/44502\"><w:r><w:t>Problem 44502. Anyone for tennis? Your chances of winning a (standard) game</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

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>.

Solve

Solution Stats

39 Solutions
4 Solvers

Last Solution submitted on Oct 07, 2021

Last 200 Solutions

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers4

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

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

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author32

Problem Tags

Community Treasure Hunt

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

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers4

Suggested Problems

More from this Author32

Problem Tags

Community Treasure Hunt

Players