Basic simulation of a series of the Monty Hall Problem

monty_hall.rb

# ######################################################################################################################
# The Monty Hall Problem #
# ########################
#
# The Premise:
#   Three identical boxes are presented to a player
#   Two are duds, and one contains a prize
#   The player chooses one box, having no idea of what it might contain.
#     In this instance, each box has a 33.3% chance of being a winner, and a 66.6% chance of being a dud (RIP 0.1%)
#   A moderator then removes one of the duds from play, leaving the players original choice, and one other box
#     In this instance, the other box now has a 50% chance of being a winner, but your original choice still only has 33.3%
#   Given these new odds, the player should take the other box every time instead of staying with their original choice.
#
# The Experiment:
#   The following code will run a series of simulations, with an array of two `0`s, and one `1`
#   The computer will randomly select a box, which will be recorded as a "held" box
#   The computer will select a dud and remove it from the array
#   The computer will then record the remaining box as a "final" box
#
# The Hypothesis:
#   I expect the simulation to hold up to game theory, and the ratio of winning "held":"final" boxes should be 50:33.3
#
# The Result (tentative):
#   It appears that running this code produces a ratio in the range of 1.5 - 2.5, with no obvious predictability
#
# The Result after some research
#   After running a much higher number of series (in the millions), the sim produces an ratio of ~2:1 reliably
#   ManLab's assumption of 3:2 and 'experiment' were both faulty - a lesson in running limited series experiments
#   It appears that 2:1 is the expected ratio - https://en.wikipedia.org/wiki/Monty_Hall_problem

@held_boxes = []
@final_boxes = []
@number_of_series = 1000000

@number_of_series.times do
  # Set up the boxes w/2 duds and a winner, then randomize the order
  boxes = [0,0,1].shuffle!
  # Held boxes gets a truly random choice
  @held_boxes << boxes.delete_at(rand(boxes.length))
  # Remove one of the duds from the equation
  boxes.delete_at(boxes.index(0))
  # Final boxes gets the last choice
  @final_boxes << boxes.pop
  # Sanity Check 1
  raise "element still exists in boxes array" if boxes.size > 0
end

# Sanity Check 2
puts @held_boxes.size == @final_boxes.size

# Remove duds, leaving a count
@held_boxes.reject! {|e| e == 0}
@final_boxes.reject! {|e| e == 0}

puts "Original estimate: 50/33.3 = #{50.0/33.3}"
puts "Updated Estimate: 66.6/33.3 = #{66.6/33.3}"
puts "Actual Result: Final Boxes / Held Boxes = #{@final_boxes.size.to_f / @held_boxes.size.to_f}"