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A demonstration of the Monty Hall Problem (http://en.wikipedia.org/wiki/Monty_Hall_problem).
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#!/usr/bin/env ruby | |
# encoding: utf-8 | |
# | |
# A silly script to demonstrate the Monty Hall Problem. | |
# http://en.wikipedia.org/wiki/Monty_Hall_problem | |
# | |
# Usage | |
# ruby [-v] monty.rb <n> | |
# where n is the number of times each of the 3 players plays the game. | |
# | |
# From [Wikipedia](http://en.wikipedia.org/wiki/Monty_Hall_problem): | |
# > Suppose you're on a game show, and you're given the choice of three doors: | |
# > Behind one door is a car; behind the others, goats. | |
# > You pick a door, say No. 1, and the host, who knows what's behind the doors, | |
# > opens another door, say No. 3, which has a goat. | |
# > He then says to you, "Do you want to pick door No. 2?" | |
# > Is it to your advantage to switch your choice? | |
# | |
# Oddly enough, the answer is that you have a 66% chance of winning if you switch to | |
# the other closed door, 33% if you stay put, and roughly 50% if you randomly | |
# change (as expected). | |
# | |
# The script demonstrates that with Alice (who always switches), Bob (who never switches), | |
# and Cecil, who does what he likes. | |
class Game | |
class Door | |
attr_accessor :open, :prize, :label | |
def initialize(game, prize) | |
@game = game | |
@prize = prize | |
@chosen = @open = false | |
end | |
end | |
class Player | |
@@players = [] | |
attr_accessor :name, :plays, :wins | |
def initialize(name, switch = nil) | |
@name = name | |
@plays = 0.0 | |
@wins = 0.0 | |
@switch = switch | |
@@players << self unless @@players.include?(self) | |
end | |
def policy | |
case @switch | |
when nil then "sometimes switches" | |
when true then "ALWAYS switches" | |
when false then "NEVER switches" | |
end | |
end | |
def to_s | |
w = @@players.map { |p| p.name.length }.max | |
x = @@players.map { |p| p.policy.length }.max + 2 | |
y = ($n || 1000000).to_s.length | |
success = ((wins / plays) * 100).round(2) | |
"%#{w}s %-#{x}s - %#{y}d/%-#{y}d %3.2f%% " % [name, policy, wins, plays, success] | |
end | |
def switch? | |
if @switch.nil? | |
[true, false].shuffle.first | |
else | |
@switch | |
end | |
end | |
def play | |
Game.play(self) | |
end | |
end | |
def initialize | |
@doors = [ | |
Door.new(self, 'Goat'), | |
Door.new(self, 'Goat'), | |
Door.new(self, 'Car') | |
].shuffle | |
@doors[0].label = 'A' | |
@doors[1].label = 'B' | |
@doors[2].label = 'C' | |
end | |
def puts(*args) | |
STDOUT.puts(*args) if $VERBOSE | |
end | |
def play(player) | |
puts | |
puts "Three doors, two goats, one car..." | |
@choice = @doors.shuffle.first | |
puts "#{player.name} chooses door #{@choice.label}" | |
door = @doors.reject { |d| d == @choice || d.prize == 'Car' }.shuffle.first | |
puts "Monty opens door #{door.label} to reveal a #{door.prize}" | |
door.open = true | |
if player.switch? | |
@choice = @doors.reject { |d| d == @choice }.reject { |d| d.open }.shuffle.first | |
puts "#{player.name} changes mind, and chooses door #{@choice.label}" | |
else | |
puts "#{player.name} stays on door #{@choice.label}" | |
end | |
puts "Monty opens door #{@choice.label}, to reveal a #{@choice.prize}" | |
if @choice.prize == 'Car' | |
puts "Congratulations!!" | |
player.wins += 1 | |
else | |
puts "Sorry..." | |
end | |
player.plays += 1 | |
end | |
def self.play(player) | |
new.play(player) | |
end | |
end | |
$n = Integer(ARGV[0] || 100) | |
alice = Game::Player.new(ARGV[1] || "Alice", true) | |
bob = Game::Player.new(ARGV[2] || "Bob", false) | |
cecil = Game::Player.new(ARGV[3] || "Cecil", nil) | |
$n.times { alice.play; print "\r#{alice}" } | |
puts | |
$n.times { bob.play; print "\r#{bob}" } | |
puts | |
$n.times { cecil.play; print "\r#{cecil}" } | |
puts |
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