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 Cody 1260 RISK Board Game Battle Simulation
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