Monte Carlo Simulation in Python

Problem:
Suppose you flip coins for a certain times, say n. You want to know your chance of getting certain number of heads in a row, say k heads in a row.

Let's start with the function that'll do a certain number of coin flips:

	def do_n_flips(n):
	return ''.join([str(random.getrandbits(1)) for i in range(n)])

view raw do_n_flips.py hosted with ❤ by GitHub

Let's do 10 flips right away:
do_n_flips(10)
'0100111001'

Let's suppose you get 1 euro if you get the given number of heads in a row while doing a certain number of flips. Here's the function that'll calculate your payoff:

	def payoff(n, k):
	if do_n_flips(n).find(''.rjust(k, '0')) > -1:
	return 1.0
	else:
	return 0.0

view raw payoff.py hosted with ❤ by GitHub

Let's try our payoff function with doing 10 flips and getting payed for 3 heads in a row. sometimes it is 0, sometimes it is 1:
payoff(10, 3)
0.0
payoff(10, 3)
1.0

Now, what is your chance to get your 1 euro for 3 heads in a row from 10 flips? This brings us to the Monte Carlo simulation, which I'wont describe here at all, just give you a function which answers our question regarding the chance:

	def monte_carlo_solve(n, k, j):
	ret = 0.0
	for x in range(j):
	ret = ret + payoff(n, k)
	return ret / j

view raw monte_carlo_solve.py hosted with ❤ by GitHub

Running with a million iteration gives us a good approximation for the chance:
monte_carlo_solve(10, 3, 1000000)
0.507753

This post was inspired by a similar post by Remis.

How to use wildcard in Google search

This example demonstrates how to use a wildcard in Google search.

Lets suppose we have this idiom: "if you have a somebody for a friend, you don't need an enemy", but we do not remember exactly what that  somebody would be.

Let's ask Google: "If you have a * for a friend, you don't need an enemy".

And here we go. For the record, at the time being, Google thinks this somebody is either a Hungarian or a politician. I assume, in fact it is a Hungarian politician :)