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Monte Carlo simulation for the Monty Hall Problem

/ Published in: Groovy
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  1. /*
  2.  * Monte Carlo simulation for the Monty Hall Problem:
  3.  * http://en.wikipedia.org/wiki/Monty_Hall_problem.
  4.  */
  5.  
  6. import java.util.*
  7.  
  8. class MontyHall {
  9.     static def RANDOM = new Random()
  10.  
  11.     def doors = ['car','goat','goat']
  12.  
  13.     MontyHall() {
  14.         Collections.shuffle(doors)
  15.     }
  16.  
  17.     def pick_door() {
  18.         RANDOM.nextInt(3)
  19.     }
  20.  
  21.     def reveal_door(pick) {
  22.         def available_doors = [0, 1, 2] - [doors.indexOf('car'), pick]
  23.         available_doors[RANDOM.nextInt(available_doors.size())]
  24.     }
  25.  
  26.     // Return true if the player won by staying
  27.     // with their first choice, false otherwise.
  28.     def staying_wins(pick) {
  29.         won(pick)
  30.     }
  31.  
  32.     // Return true if the player won by switching, false otherwise.
  33.     def switching_wins(pick, open_door) {
  34.         def switched_pick = ([0, 1, 2] - [open_door, pick])[0]
  35.         won(switched_pick)
  36.     }
  37.  
  38.     // Return true if the player's final pick hides a car, false otherwise.
  39.     def won(pick) {
  40.         doors[pick] == 'car'
  41.     }
  42.  
  43.     public static void main(String[] args) {
  44.         def ITERATIONS = 1000000
  45.  
  46.         def staying = 0
  47.         def switching = 0
  48.  
  49.         ITERATIONS.times {
  50.             def mh = new MontyHall()
  51.             def picked = mh.pick_door()
  52.             def revealed = mh.reveal_door(picked)
  53.             if (mh.staying_wins(picked)) staying++
  54.             if (mh.switching_wins(picked, revealed)) switching++
  55.         }
  56.  
  57.         def staying_rate = (staying / ITERATIONS) * 100
  58.         def switching_rate = (switching / ITERATIONS) * 100
  59.  
  60.         println "Staying: ${staying_rate}%."
  61.         println "Switching: ${switching_rate}%."
  62.     }
  63. }

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