# Flip a lot of coins;
# Use the distribution of longest run of zeros to infer how many
# coinflips were done, ex post facto.
import random
def generate_coinflips(num):
    return [ random.choice([0,1]) for i in range(num) ]

def longest_run_zero(x):
    i = 0
    count = 0
    max_count = 0
    while i < len(x):
        if x[i] == 0:
            count += 1
        else:
            if count > max_count:
                max_count = count
            count = 0
        i += 1
        
    return max_count

def longest_run_mc(runsize, num):
    z = []
    for i in range(num):
        x = generate_coinflips(runsize)
        count = longest_run_zero(x)
        z.append(count)
        
    return z

# do 100 runs of 1000 coinflips, and plot the distribution
d = longest_run_mc(100, 1000)
hist(d, bins=max(d), range=(0, max(d)))

# we expect a peak right around...
print math.log(100, 2)

# if we do 500 coinflips, the peak shifts right, to... 
d = longest_run_mc(500, 1000)
hist(d, bins=max(d), range=(0, max(d)))
print math.log(500, 2)