montepi

from random import random

from math import pi, fabs

accuracies = {
    '10': 0,
    '100': 0,
    '1000': 0,
    '10000': 0,
    '100000': 0,
    '1000000': 0,
    '10000000': 0,
}

num = 0
num_samples = [10, 100, 1000, 10000, 100000, 1000000, 10000000]

average_val = 0

for samples in num_samples:
    for n in range(1, 101):
        for _ in range(samples):
            x, y = random(), random()
            if x*x + y*y <= 1:
                num += 1
        average_val *= (n-1)
        average_val += 4*(float(num)/samples)
        average_val /= n
        num = 0

    print 'With ' + str(samples) + ' samples we have an error margin of ' + str(fabs(average_val - pi))