Problem 3056. Chess probability

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 difference in the ratings between two players serves as a predictor of the outcome of a match (the</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Elo_rating_system\"><w:r><w:t>Elo rating system</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>If Player A has a rating of Ra and Player B a rating of Rb, the formula for the expected score of Player A is :</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>Two players with equal ratings who play against each other are expected to score an equal number of wins. A player whose rating is 100 points greater than their opponent's is expected to score 64%; if the difference is 200 points, then the expected score for the stronger player is 76%.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>I give you two ELOs, compute the expected score (round to 3 digits), or probability that the first player wins.</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,iVBORw0KGgoAAAANSUhEUgAAAM4AAAArBAMAAADCuKrGAAAAMFBMVEX///90dHQEBAQwMDCenp5QUFAWFhbm5ubMzMyKioq2trZAQEAMDAwiIiJiYmIAAADHPVvyAAAAAXRSTlMAQObYZgAAAuJJREFUeNrtV0toE2EQ/pJs91+TZpuKKZ7aHDxZhKBo8WCNQj14qNHiAxFZRNIHVAPFi0UbFC8qEqh40cOePBUfUAoS0BQPvhByqXqoEK1CaauNXswWu3H+JF03TbV5dHPqwGYzM//u98/881qgOhoscZ29OhjnkRIXOqqCYdvmXqMmtKc2fiuZ1nHWcdZxikmrDU7Xq53hkhbagG8Nz7Cl0WO565xkuxS3/nwEHUinrMfJ9NLdbz2OPYUkVOtD+2GA+S0HEYDAzQ82nyEYe8R/+yxAfoc6671G+dM6If+U0oC4sEyXWSuQHzw5JQ0MdfRnPmxpvGk6Fam9lK5q9kzGQpwSqz4Y+beK71cq2rSDxwC9V6iPlrE/+T/GH6fLVWRPhpx3ia57v4Jl4NyIYv5pV8HODH4kx9ep0uETuOYly9m43dV/N7brShRS50xw9amWCwabaWEboO4f7THrDF4PABv4aKe3PMDn2SSJFFMi2ZSiCvt2JcFLDMNJWdYEHqV/yeB52vvBmtQRiAfjOFvQfybhWF6zWau6gkDuwXlVoD214MK0WWvwGnnHB5ZCH9gLFf1mnKvTGJpY3ivfLIWd2yRI+yAEFsnpKe+sD/fbpwL5RVkeUraeLPpxPRtdH42HS5me3SZBgwcOxRWAlEI7aSJCwhaLxR7nebjI0m76PGBRUW2C+EnBucr6djgCSaHSoSWxSDUjkolnOjo6DuV57KaYe4IDWDg9uekOxF4FxyrD4TVEEVTYPRiWcLHxfT6TcjzqGUUeWZTZuHVOCWOM4XfFc0gaepCdOglvEpvnt+djJMfLvgEIUcYFU7f1fZ344k1Wdj5DUbjjPH+yNAqxICgHvo/DFbGV2QCyOK5Q6Ewo1G+KA7diZHD3UvbnKYijuFX2V+JK9ohBiEk4cyVG1r+2FZiTkCZVDy6vAY6cQINaQV8oa6olgZaGrKwtTtFUywXa8+YdVnVDN2pDjqrf8Af8bczR/4tLjAAAAABJRU5ErkJggg=="}]}

Solve

Solution Stats

292 Solutions
108 Solvers

Last Solution submitted on May 28, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers108

Problem Tags

chess elo

Community Treasure Hunt

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

Start Hunting!

Problem 3056. Chess probability

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers108

Suggested Problems

More from this Author43

Problem Tags

Community Treasure Hunt

Problem 3056. Chess probability

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers108

Suggested Problems

More from this Author43

Problem Tags

Community Treasure Hunt

Players