monty_hall.rb

switch_strategy = 0
no_switch_strategy = 0
n_simulations = 1_000_000

n_simulations.times do
  winner_door = rand(3)
  chosen_door = rand(3)

  if winner_door == chosen_door
    switch_strategy += 0
    no_switch_strategy += 1
  else
    # The host always opens the other non-winning door and not your door, this
    # reveals 'information' about your door.
    revealed_door = [0, 1, 3] - [winner_door] - [chosen_door]
    chosen_door = winner_door
    switch_strategy += 1
    no_switch_strategy += 0
  end
end

puts "Switch strategy wins: #{switch_strategy} (#{(switch_strategy.to_f / n_simulations * 100).round(2)}%}"
puts "No Switch strategy wins: #{no_switch_strategy} (#{(no_switch_strategy.to_f / n_simulations * 100).round(2)}%)"
# Switch strategy wins: 666481 (66.65%}
# No Switch strategy wins: 333519 (33.35%)

Lines 15 and 16 are not necessary. Thanks for the great napkin math article!

Revealed door:

possible_revealed_doors = [0, 1, 2] - [winner_door] - [chosen_door]
revealed_door = possible_revealed_doors.shuffle.pop

Yep, it's there on purpose to make it easier for people to see why the strategy works :) More like prose!

The simulation here doesn't simulate the Monty Hall problem, it's just showing the probability of picking the correct door when there are 3 doors to choose from.

For example, picking the right door off the bat doesn't imply the "no switch strategy" wins.