Probability distribution of the longest run of heads or tails in N tosses of a fair coin

run_distribution_in_coin_tosses.py

# Find the probability distribution of the longest run of heads or tails in N tosses of a fair coin.

N = 10   # Number of coin tosses

from itertools import product, imap, groupby
from collections import Counter

# Adapted from http://stackoverflow.com/a/22214180/677398
def longest_run(sequence):
    return max(sum(1 for _ in group) for key, group in groupby(sequence))

coin_tosses = product('HT', repeat=N)
distribution = Counter(imap(longest_run, coin_tosses))
print sorted(distribution.items())

# Expected output: 
# [(1, 2), (2, 176), (3, 370), (4, 254), (5, 126), (6, 56), (7, 24), (8, 10), (9, 4), (10, 2)]