Chapter 4, Problem 12PP

In the land of Puzzlevania, Aaron, Bob, and Charlie had an argument over which one of them was the greatest puzzle-solver of all time. To end the argument once and for all, they agreed on a duel to the death. Aaron was a poor shot and only hit his target with a probability of 1/3. Bob was a bit better and hit his target with a probability of 1/2. Charlie was an expert marksman and never missed. A hit means a kill and the person hit drops out of the duel. To compensate for the inequities in their marksmanship skills, the three decided that they would fire in turns, starting with Aaron, followed by Bob, and then by Charlie. The cycle would repeat until there was one man standing. That man would be remembered for all time as the Greatest Puzzle-Solver of All Time. An obvious and reasonable strategy is for each man to shoot at the most accurate shooter still alive, on the grounds that this shooter is the deadliest and has the best chance of hitting back.

Write a program to simulate the duel using this strategy. Your program should use random numbers and the probabilities given in the problem to determine whether a shooter hits his target. You will likely want to create multiple subroutines and functions to complete the problem. Once you can simulate a duel, add a loop to your program that simulates 10,000 duels. Count the number of times that each contestant wins and print the probability of winning for each contestant (e.g., for Aaron your program might output "Aaron won 3595/10,000 duels or 35.95%").

An alternate strategy is for Aaron to intentionally miss on his first shot. Modify the program to accommodate this new strategy and output the probability of winning for each contestant. What strategy is better for Aaron, to intentionally miss on the first shot or to try and hit the best shooter?