Problem 52110. Pick the die most likely to win

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>After discussing </w:t></w:r><w:hyperlink w:docLocation=\"https://www.mathworks.com/matlabcentral/cody/problems/46072-rock-paper-scissors-lizard-spock\"><w:r><w:t>Rock, Paper, Scissors, Lizard, Spock</w:t></w:r></w:hyperlink><w:r><w:t> in </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>The Simpsons and their Mathematical Secrets</w:t></w:r><w:r><w:t>, Simon Singh writes that investor Warren Buffett will challenge people to beat him in a game of dice. He presents three dice and asks the other person to choose one. Then he chooses one, and they roll together. The person with the highest roll wins. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>With standard dice that have one to six pips on their sides, no one has an advantage. However, Mr. Buffett’s dice are different: Although the sum of the numbers on the faces of one die equals the sums for the other dice, the numbers on one die differ from the numbers on the other dice.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>For example, suppose die A has 1, 1, 6, 6, 8, and 8; die B has 3, 3, 5, 5, 7, and 7; and die C has 2, 2, 4, 4, 9, and 9. If the first person chooses die A, then Warren Buffett will choose die C to increase his chances of winning. </w:t></w:r><w:r><w:t>Write a function that choose the die most likely to win, given the other person’s choice. The input is a matrix with the numbers on the faces of each die in the rows and an index of the die (i.e., row) that the other person chose.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 228px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 114px; transform-origin: 407px 114px; vertical-align: baseline; "><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 51.3417px 7.79167px; transform-origin: 51.3417px 7.79167px; unicode-bidi: normal; "><span style="">After discussing </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/46072-rock-paper-scissors-lizard-spock"><span style=""><span style="">Rock, Paper, Scissors, Lizard, Spock</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.33333px 7.79167px; transform-origin: 9.33333px 7.79167px; unicode-bidi: normal; "><span style=""> in </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 143.142px 7.79167px; transform-origin: 143.142px 7.79167px; unicode-bidi: normal; "><span style="font-style: italic; ">The Simpsons and their Mathematical Secrets</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 65.45px 7.79167px; transform-origin: 65.45px 7.79167px; unicode-bidi: normal; "><span style="">, Simon Singh writes that investor Warren Buffett will challenge people to beat him in a game of dice. He presents three dice and asks the other person to choose one. Then he chooses one, and they roll together. The person with the highest roll wins. </span></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 362.242px 7.79167px; transform-origin: 362.242px 7.79167px; unicode-bidi: normal; "><span style="">With standard dice that have one to six pips on their sides, no one has an advantage. However, Mr. Buffett’s dice are different: Although the sum of the numbers on the faces of one die equals the sums for the other dice, the numbers on one die differ from the numbers on the other dice.</span></span></div><div style="block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376.833px 7.79167px; transform-origin: 376.833px 7.79167px; unicode-bidi: normal; "><span style="">For example, suppose die A has 1, 1, 6, 6, 8, and 8; die B has 3, 3, 5, 5, 7, and 7; and die C has 2, 2, 4, 4, 9, and 9. If the first person chooses die A, then Warren Buffett will choose die C to increase his chances of winning. </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 64.0417px 7.79167px; transform-origin: 64.0417px 7.79167px; unicode-bidi: normal; "><span style="">Write a function that choose the die most likely to win, given the other person’s choice. The input is a matrix with the numbers on the faces of each die in the rows and an index of the die (i.e., row) that the other person chose.</span></span></div></div></div>

After discussing Rock, Paper, Scissors, Lizard, Spock in The Simpsons and their Mathematical Secrets, Simon Singh writes that investor Warren Buffett will challenge people to beat him in a game of dice. He presents three dice and asks the other person to choose one. Then he chooses one, and they roll together. The person with the highest roll wins. 
With standard dice that have one to six pips on their sides, no one has an advantage. However, Mr. Buffett’s dice are different: Although the sum of the numbers on the faces of one die equals the sums for the other dice, the numbers on one die differ from the numbers on the other dice.
For example, suppose die A has 1, 1, 6, 6, 8, and 8; die B has 3, 3, 5, 5, 7, and 7; and die C has 2, 2, 4, 4, 9, and 9. If the first person chooses die A, then Warren Buffett will choose die C to increase his chances of winning. Write a function that choose the die most likely to win, given the other person’s choice. The input is a matrix with the numbers on the faces of each die in the rows and an index of the die (i.e., row) that the other person chose.

Solve

Solution Stats

15 Solutions
6 Solvers

Last Solution submitted on Jul 30, 2021

Last 200 Solutions

Problem Recent Solvers6

Problem Tags

dice nontransitive probability

Community Treasure Hunt

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

Start Hunting!

Problem 52110. Pick the die most likely to win

Solution Stats

Last 200 Solutions

Problem Recent Solvers6

Suggested Problems

More from this Author131

Problem Tags

Community Treasure Hunt

Problem 52110. Pick the die most likely to win

Solution Stats

Last 200 Solutions

Problem Recent Solvers6

Suggested Problems

More from this Author131

Problem Tags

Community Treasure Hunt

Players