Demonstration of the Monty Hall problem and that a switching strategy is always better ( you win 2/3 of the time).

monty.rb

class Monty
  STAY = true
  SWITCH = false

  def initialize(strat = STAY)
    @strategy = strat
    @times_won = 0
  end

  def play(n)
    n.times do
      choices = self.doors
      first_pick = rand(3)
      # eliminate the door that was not picked and is not a car.
      choices.each_with_index { |choice, door| choices[door] = nil if first_pick != door and choice != "car" }
      self.outcome(first_pick, choices)
    end
    puts "You won %d%% of the time with a %s strategy." % [((@times_won.to_f / n) * 100), @strategy ? "staying" : "switching"]
  end

  protected
  def doors
    ["car", "goat", "goat"].shuffle
  end

  def outcome(first_pick, choices)
    if @strategy
      # Staying strategy, just examine our first pick
      @times_won += choices[first_pick] == "car" ? 1 : 0
    else
      # Switch strategy, eliminate our choice and check the remaininder
      choices[first_pick] = nil
      choices.compact!
      @times_won += choices.first == "car" ? 1 : 0
    end
  end
end

game = Monty.new(Monty::STAY)
game.play(100000)

game = Monty.new(Monty::SWITCH)
game.play(100000)

# OUTPUT:
# You won 33% of the time with a staying strategy.
# You won 66% of the time with a switching strategy.