Monty Hall problem where host picks randomly - based on https://gist.github.com/alexaandru/1926859

monty_hall_modified.rb

#
# This class creates a model of the Monty Hall problem.
# It simulates arranging the set with prize/goats, both guest
# and Monty picking a door and then the decision to switch
# or not to switch (and of course, the outcome).
#
# Each instance of the class (MontyHall.new) runs a new
# show. Sample usage code is at the bottom.
#
class MontyHall
  attr_accessor :doors, :result

  #
  # We start with three doors, randomly sorted.
  # Then we run through the entire scenario as
  # outlined below.
  #
  def initialize(do_switch = true, show_backstage = false)
    @doors          = [0, 1, 2].sort_by { rand }
    @doors_content  = Array.new(3)
    @do_switch      = do_switch
    @show_backstage = show_backstage

    set_the_stage
    guest_pick
    monty_pick
    guest_decide_to_switch_or_not
    determine_outcome
  end

  #
  # Set the stage: put a prize behind one door,
  # a goat behind the two remaining doors.
  #
  def set_the_stage
    # put a prize at a random door
    @doors_content[rand(3)] = :prize
    # put a goat on all other doors
    3.times { |i| @doors_content[i] ||= :goat }
  end

  #
  # Guest takes his pick.
  #
  def guest_pick
    # The doors are already randomly sorted, so we just
    # pop out a door from the top of the stack.
    @guest_pick = @doors.pop
  end

  #
  # Monty takes his pick, always picking a :goat
  # door.
  #
  def monty_pick

    # always pick d1
    # comment these three lines to use original MH problem
    @monty_pick = @doors.first
    @remaining_door = @doors.last
    return

    d1, d2 = @doors.sort_by { rand }

    # And we also make sure that we have a goat
    # behind the door Monty opens.
    if @doors_content[d1].eql?(:goat)
      @monty_pick = d1
      @remaining_door = d2
    else
      @monty_pick = d2
      @remaining_door = d1
    end
  end

  def guest_decide_to_switch_or_not(_do_switch = @do_switch)
    @guest_pick, @remaining_door = @remaining_door, @guest_pick if @do_switch
  end

  def determine_outcome
    @result = if @doors_content[@monty_pick].eql? :prize
                nil
              elsif @doors_content[@guest_pick].eql?(:prize)
                true
              else
                false
              end
  end
end

# This controls the number of shows we play
no_of_shows = 100_000

# This controls the switching decision, can be set to: true or false
# It will be used for ALL shows we run at once.
do_switch = false

# Show backstage tips. Don't set it unless you run really small loops.
show_backstage = false

# This counts the success/failure of all shows we played
success = 0
failure = 0

# This runs all the shows we asked for
no_of_shows.times do
  result = MontyHall.new(do_switch, show_backstage).result
  success += 1 if result === true
  failure += 1 if result === false
end

# And finally, we compute & display the rate
puts 'Success rate when we %s switch is: %.2f%' % [do_switch ? 'do' : "don't", ((success * 100.0) / (success + failure))]