The St. Louis Cardinals won the world series last night. I wish I had some emotional interest in either team as there was some great baseball played, and the two teams needed seven games to decide the final winner.

In that spirit, John Allen Paulos (the author of Innumeracy) tweeted earlier this week an interesting probability question:

Well, my intuition was stuck in the mud with this question so I did do some calculating. And like any good stats teacher with a frequentist view of probability, I simulated the World Series one million times with the following Python script:

import random

trials = 1000000
games = [0,0,0,0]

for n in range(0,trials):
	play = True
	a,b = 0,0
	while play:
		if random.randint(0,1):
			a = a + 1
		else:
			b = b + 1

		if a == 4 or b == 4:
			g = a + b
			games[g-4] = games[g-4] + 1
			play = False

for i in range(0,len(games)):
	print i+4, "games:", games[i]/float(trials)

The results:

4 games: 0.125343
5 games: 0.249538
6 games: 0.312847
7 games: 0.312272

So there’s definitely no reason to believe the chances are not equal.

Of course, there’s something to be said for using some simple reasoning: