Simulating the birthday paradox.

birthday.rb

#!/usr/bin/env ruby

require 'optparse'

def parse_options
  options = { }
  OptionParser.new { |opts|
    opts.banner = "Usage: #{__FILE__} --group-size G --trial-count T"
    opts.on('-g', '--group-size size', 'Size of the group') { |v| options[:group_size] = v }
    opts.on('-t', '--trial-count count', 'How many trials to run') { |v| options[:trial_count] = v }
  }.parse!
  raise OptionParser::MissingArgument.new if [:group_size, :trial_count].any? { |v| options[v].nil? }
  options
end

def to_percentage(numer, denom)
  decimal = numer.to_f / denom
  (decimal * 100).round(4).to_s + '%'
end

def shared_birthday?(group_size)
  # Generate an array with size `group_size`, and randomly assign every member a birthday.
  # Return true if two members share a birthday; else return false.
  counter   = Hash.new 0
  birthdays = group_size.times.map { rand 365 }
  birthdays.each do |birthday|
    counter[birthday] += 1
    return true if counter[birthday] > 1
  end
  false
end

def run_birthday_trials(group_size, trial_count)
  # Run the shared_birthday? experiment `trial_count` times.
  # Return the number of experiments which resulted in a shared birthday.
  successes = 0
  trial_count.times { successes += 1 if shared_birthday? group_size }
  successes
end


if __FILE__ == $0
  options     = parse_options
  group_size  = options[:group_size].to_i
  trial_count = options[:trial_count].to_i
  successes   = run_birthday_trials group_size, trial_count

  puts <<-EOS.gsub!(/^ +/, '')
    Using a group size of #{group_size} people, in #{trial_count} independent trials, at least
    two people shared a birthday in #{successes} of those trials.

    In other words, within a group of #{group_size} people, the probability that two people share
    a birthday is #{to_percentage successes, trial_count}.
  EOS
end