Problem 3061. Mirror, mirror on the wall, who is fairest of them all?

Created by Jean-Marie Sainthillier

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":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","targetMode":"","relationshipId":"rId1","target":"/media/image1.png"}],"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>The Elo rating system was featured in the movie</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>The Social Network</w:t></w:r><w:r><w:t> during the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"https://www.youtube.com/watch?v=BzZRr4KV59I/\"><w:r><w:t>algorithm scene</w:t></w:r></w:hyperlink><w:r><w:t> where Mark Zuckerberg released Facemash.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>In the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. The Elo system is employed to rank coeds by their attractiveness. The equations driving the algorithm are shown briefly (Ea and Eb).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You should know these equations now (See problem</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/3056-chess-probability/\"><w:r><w:t>3056</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:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Ea is the expected probability that Girl A will win the match against Girl B.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Ra is the rating of Girl A, which changes after tournament, according to the formula (Ra )n = (Ra )n-1 + 32 (W - Ea ) where W = {1,0.5,0}.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Now imagine a single round-robin tournament where each girl plays (is compared with) every other girl once. A judge (me for the problem) gives a note :</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>1 if girl A is more attractive than girl B</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>0 if girl B is more attractive than girl A</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>0.5 if same attractiveness</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>I give you the tournament results (2 on the main diagonal).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Find the final rating of Snow White (she is unique).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Consider that all girl begin the tournament with a rating of 1000.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You can observe that the total number of attractiveness (ELO) points remains constant.</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>"},{"partUri":"/media/image1.png","contentType":"image/png","content":"data:image/png;base64,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"}]}

The Elo rating system was featured in the movie The Social Network during the <a href = "https://www.youtube.com/watch?v=BzZRr4KV59I/">algorithm scene</a> where Mark Zuckerberg released Facemash.In the scene Eduardo Saverin writes mathematical formulas for the Elo rating system on Zuckerberg's dorm room window. 
The Elo system is employed to rank coeds by their attractiveness. 
The equations driving the algorithm are shown briefly (Ea and Eb).You should know these equations now (See problem <a href = "http://www.mathworks.com/matlabcentral/cody/problems/3056-chess-probability/">3056</a>) :<img src = "http://upload.wikimedia.org/math/b/0/3/b0366725c224ee55eab6e2371dc6a0ef.png"><ul><li></li></ul>Ea is the expected probability that Girl A will win the match against Girl B.Ra is the rating of Girl A, which changes after tournament, according to the formula (Ra )n = (Ra )n-1 + 32 (W - Ea ) where W = {1,0.5,0}.Now imagine a single round-robin tournament where each girl plays (is compared with) every other girl once.
A judge (me for the problem) gives a note :<ul><li>1 if girl A is more attractive than girl B</li><li>0 if girl B is more attractive than girl A</li><li>0.5 if same attractiveness</li></ul>I give you the tournament results (2 on the main diagonal).Find the final rating of Snow White (she is unique).Consider that all girl begin the tournament with a rating of 1000.You can observe that the total number of attractiveness (ELO) points remains constant.

Solve

Solution Stats

12 Solutions
10 Solvers

Last Solution submitted on Sep 04, 2020

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Rafael S.T. Vieira on 4 Sep 2020 at 20:49

The score should be updated only after all matches. I initially thought that it should be updated after each tournament round (that's how it is done while playing on the net, but I guess each tournament has its rules).

Problem Recent Solvers10

Problem Tags

chess elo the social network

Problem 3061. Mirror, mirror on the wall, who is fairest of them all?

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers10

Suggested Problems

More from this Author43

Problem Tags

Problem 3061. Mirror, mirror on the wall, who is fairest of them all?

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers10

Suggested Problems

More from this Author43

Problem Tags

Players