Monty Hall Problem Simulator

0-readme.md

The Monty Hall Problem is a probability puzzle.

When i read this article about Marilyn vos Savant, my initial reaction was "that can't be right". I continued to read the comments, the wikipedia page and then started a table to see if this was indeed the case. Being a programmer, i then started a simulation.

This is what it turned out to be.

The concise explanation is: The door's chance does not change. This became apparent right when i started coding. Maybe it helps anyone else understanding the problem, and also the general brainfuck that is probability.

monty_hall.rb

# This code is Licensed under CC-0 / Public Domain / WTFPL
# Written by Claudius Coenen <opensource@amenthes.de>
# Related reading:
# - http://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/
# - http://en.wikipedia.org/wiki/Monty_Hall_problem

class MontyHall
  def initialize(doors, eliminations)
    @available_doors = (0...doors).to_a
    @prize_door = @available_doors[rand(doors)]
    @eliminations = eliminations
  end

  def run
    @initial_choice = choose_random
    puts "Prize at #{@prize_door}, You're selecting #{@initial_choice}." if VERBOSITY > 1
    print_choices if VERBOSITY > 3

    host_eliminates = eliminate_doors_except([@initial_choice])
    puts "  Host eliminates #{host_eliminates.join(', ')}." if VERBOSITY > 2
    print_choices if VERBOSITY > 3

    @available_doors.delete @initial_choice
    @altered_choice = choose_random
    puts "  Choice changed to #{@altered_choice}." if VERBOSITY > 2 && @altered_choice != @initial_choice
  end

  def choose_random
    @available_doors[rand(@available_doors.length)]
  end

  def eliminate_doors_except(exceptions)
    elimination_candidates = @available_doors - exceptions - [@prize_door]
    host_eliminates = []
    @eliminations.times do
      eliminate = elimination_candidates.delete_at rand(elimination_candidates.length)
      host_eliminates.push eliminate
    end
    @available_doors -= host_eliminates
    host_eliminates
  end

  def print_choices
    puts "  Your current choices are #{@available_doors.join(', ')}."
  end

  def initial_choice_correct?
    @initial_choice == @prize_door
  end

  def altered_choice_correct?
    @altered_choice == @prize_door
  end
end

VERBOSITY = 1
iterations = 10000

(3..5).to_a.each do |doors|
  (0..3).to_a.each do |eliminations|
    # you can't run this test unless you have anything to switch to. (doors must be at least eliminations + 2)
    next if eliminations > doors - 2

    puts "Monty Hall with #{iterations} iterations of #{doors} doors and #{eliminations} eliminations" if VERBOSITY > 0
    win_by_keeping = 0
    win_by_switching = 0

    iterations.times do
      mh = MontyHall.new(doors, eliminations)
      mh.run
      win_by_keeping += 1 if mh.initial_choice_correct?
      win_by_switching += 1 if mh.altered_choice_correct?
    end

    puts "  Keeping wins #{win_by_keeping}/#{iterations} times" if VERBOSITY > 0
    puts "  Switching wins #{win_by_switching}/#{iterations} times" if VERBOSITY > 0
  end
end

output

Slightly formatted sample output for 10000 iterations

Monty Hall with 10000 iterations of 3 doors and 0 eliminations
  Keeping wins 3297/10000 times
  Switching wins 3392/10000 times

Monty Hall with 10000 iterations of 3 doors and 1 eliminations
  Keeping wins 3308/10000 times
  Switching wins 6692/10000 times


Monty Hall with 10000 iterations of 4 doors and 0 eliminations
  Keeping wins 2516/10000 times
  Switching wins 2536/10000 times

Monty Hall with 10000 iterations of 4 doors and 1 eliminations
  Keeping wins 2510/10000 times
  Switching wins 3740/10000 times

Monty Hall with 10000 iterations of 4 doors and 2 eliminations
  Keeping wins 2527/10000 times
  Switching wins 7473/10000 times


Monty Hall with 10000 iterations of 5 doors and 0 eliminations
  Keeping wins 2020/10000 times
  Switching wins 1986/10000 times

Monty Hall with 10000 iterations of 5 doors and 1 eliminations
  Keeping wins 1945/10000 times
  Switching wins 2715/10000 times

Monty Hall with 10000 iterations of 5 doors and 2 eliminations
  Keeping wins 1984/10000 times
  Switching wins 3957/10000 times

Monty Hall with 10000 iterations of 5 doors and 3 eliminations
  Keeping wins 2076/10000 times
  Switching wins 7924/10000 times