Alex Bellos' method of winning a guessing game

bellos.py

#!/usr/bin/env python3

"""	Test Alex Bellos' method of winning a guessing game.
	
	Take two random numbers, a and b.  The objective is to
	guess whether a is greater than or less than b.
	
	You might think you have a 50% chance of guessing correctly,
	which is true if guessed randomly.
	
	However, Alex Bellos on Numberphile suggests a different method:
	Pick a third random number, k, and instead pretend k is b.
	Compare a against k and use this to decide how a compares to b.
	
	This is unintuitive, so the best way to check is to simulate.
	
	Reference: https://www.youtube.com/watch?v=ud_frfkt1t0
"""

import sys
import random

random.seed()

def random_guess(a, k):
	"""	Return '<' or '>' randomly.
		Should be 50% probability of being right.
		Does not look at k.
	"""
	return random.choice(('<', '>'))

def bellos_guess(a, k):
	"""	Return Alex Bellos' educated guess.
		Generate random number and guess against that instead.
		Allegedly >50% probability of being right.
	"""
	if a < k:
		return '<'
	if a > k:
		return '>'

	raise ValueError

def simulation(guess_method, samples):
	correctness = 0

	for i in range(samples):

		# get three unique integers from range 1-99
		a, b, k = random.sample( range(1,100), 3 )

		# don't tell the method what b is
		guess = guess_method(a, k)

		correct = (a < b) == (guess == '<')
		if correct:
			correctness += 1

	return correctness / samples * 100

if __name__ == '__main__':
	try:
		samples = int(sys.argv[1])
	except (IndexError, ValueError):
		samples = 1000000 # default to one million samples

	print("Running simulation with %d samples" % samples)

	print(
		"\tRandom guess = %f%% correctness"
		% simulation(random_guess, samples=samples)
	)
	print(
		"\tBellos guess = %f%% correctness"
		% simulation(bellos_guess, samples=samples)
	)