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

Created by Richard Zapor

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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>

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 <http://www.mathworks.com/matlabcentral/cody/problems/1260-risk-board-game-battle-simulation/solutions/map Cody 1260 RISK Board Game Battle Simulation>

<http://en.wikipedia.org/wiki/Risk_%28game%29#Official Link to official Risk Rules>

*Simplified explanation of the dice play:*
  
  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.
  
  Defense with 1 army will use one die.
  Defense with 2 or more armies will throw 2 die.
  
  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).

*Input:* a,d where a is number of attacking armies and d is number defending

*Output:* pwin, the probability of the Attacker Winning

*Accuracy:* Accurate to +/- 1e-6

*Scoring:* Time (msec) to solve 10 Battle Scenarios

<http://recreationalmath.com/Risk/ Risk Calculator>

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Last Solution submitted on Feb 24, 2021

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

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

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