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Monty Hall empirical proof
require 'test/unit'
# Read about the problem and mathematical proof here:
# http://www.greenteapress.com/thinkbayes/html/thinkbayes002.html#sec15
class MontyHall
include Test::Unit::Assertions
NUM_DOORS = 3
# @return [Boolean] whether player won
def play
winning_door = rand(NUM_DOORS)
player_first_choice = rand(NUM_DOORS)
opened_empty_door = open_empty_door(winning_door, player_first_choice)
assert_not_equal winning_door, opened_empty_door
assert_not_equal player_first_choice, opened_empty_door
player_second_choice = second_choice(player_first_choice, opened_empty_door)
return (player_second_choice == winning_door)
end
end
# basic Monty Hall rules, player always switches doors
class MontyHallStandard < MontyHall
def open_empty_door(winning_door, player_first_choice)
((0...NUM_DOORS).to_a - [winning_door, player_first_choice]).sample
end
# always switch doors
def second_choice(player_first_choice, opened_empty_door)
((0...NUM_DOORS).to_a - [player_first_choice, opened_empty_door]).sample
end
end
class MontyHallAlwaysB < MontyHallStandard
PREFERRED_DOOR = 1
def open_empty_door(winning_door, player_first_choice)
forbidden_doors = [winning_door, player_first_choice]
if forbidden_doors.include?(PREFERRED_DOOR)
super
else
PREFERRED_DOOR
end
end
end
class MontyHallAlwaysBPlayerStick < MontyHallAlwaysB
def second_choice(player_first_choice, opened_empty_door)
opened_empty_door == PREFERRED_DOOR ? player_first_choice : super
end
end
attempts = 10000
# game = MontyHallStandard.new
# game = MontyHallAlwaysB.new
game = MontyHallAlwaysBPlayerStick.new
successes = attempts.times.count { game.play }
success_rate = successes.to_f/attempts
puts "player success rate #{success_rate} in #{attempts} attempts"
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