Problem 1301. RISK Calculator - Large Armies, High Accuracy, Fast

Created by Richard Zapor

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>This Challenge is to quickly provide the high precision probability of legal RISK battles up to 100 vs 100. [ Attack &gt;= 2 and Defense &gt;=1 ].</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Related to </w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/1260-risk-board-game-battle-simulation/solutions/map\"><w:r><w:t>Cody 1260 RISK Board Game Battle Simulation</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Risk_%28game%29#Official\"><w:r><w:t>Link to official Risk Rules</w:t></w:r></w:hyperlink></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Simplified explanation of the dice play:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[Attacker with 2 armies will throw one die.\nAttacker with 3 armies will throw two die.\nAttacker with 4 or more armies will throw three die.\n\nDefense with 1 army will use one die.\nDefense with 2 or more armies will throw 2 die.\n\nThe attacker High is compared to the Defender High.\nIf Attacker High > Defender High then defender loses 1 army otherwise Attacker loses 1 army. Tie goes to defender.\nIf the Defender threw two die and the Attacker threw 2 or more die then the Second Highest of each is compared. \nIf Attack > Defense then Defense loses an army otherwise Attack loses an army.\nAttack continues until No defenders remain (Win) or Attack is reduced to 1 army (Lose).]]></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>Input:</w:t></w:r><w:r><w:t> a,d where a is number of attacking armies and d is number defending</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>Output:</w:t></w:r><w:r><w:t> pwin, the probability of the Attacker Winning</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>Accuracy:</w:t></w:r><w:r><w:t> Accurate to +/- 1e-6</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>Scoring:</w:t></w:r><w:r><w:t> Time (msec) to solve 10 Battle Scenarios</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"http://recreationalmath.com/Risk/\"><w:r><w:t>Risk Calculator</w:t></w:r></w:hyperlink></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>"}]}

This Challenge is to quickly provide the high precision probability of legal RISK battles up to 100 vs 100. [ Attack >= 2 and Defense >=1 ].Related to <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1260-risk-board-game-battle-simulation/solutions/map">Cody 1260 RISK Board Game Battle Simulation</a><a href = "http://en.wikipedia.org/wiki/Risk_%28game%29#Official">Link to official Risk Rules</a>Simplified explanation of the dice play:<pre class="language-matlab">Attacker with 2 armies will throw one die.
Attacker with 3 armies will throw two die.
Attacker with 4 or more armies will throw three die.
</pre><pre class="language-matlab">Defense with 1 army will use one die.
Defense with 2 or more armies will throw 2 die.
</pre><pre class="language-matlab">The attacker High is compared to the Defender High.
If Attacker High > Defender High then defender loses 1 army otherwise Attacker loses 1 army. Tie goes to defender.
If the Defender threw two die and the Attacker threw 2 or more die then the Second Highest of each is compared. 
If Attack > Defense then Defense loses an army otherwise Attack loses an army.
Attack continues until No defenders remain (Win) or Attack is reduced to 1 army (Lose). 
</pre>Input: a,d where a is number of attacking armies and d is number defendingOutput: pwin, the probability of the Attacker WinningAccuracy: Accurate to +/- 1e-6Scoring: Time (msec) to solve 10 Battle Scenarios<a href = "http://recreationalmath.com/Risk/">Risk Calculator</a>

Solve

Solution Stats

69 Solutions
23 Solvers

Last Solution submitted on Aug 24, 2020

Last 200 Solutions

Problem Comments

Problem Recent Solvers23

Problem Tags

markov chain recursion risk speed scoring

Problem 1301. RISK Calculator - Large Armies, High Accuracy, Fast

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers23

Suggested Problems

More from this Author236

Problem Tags

Problem 1301. RISK Calculator - Large Armies, High Accuracy, Fast

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers23

Suggested Problems

More from this Author236

Problem Tags

Players