Coin Flip Problem

hh_or_ht.py

import random

def flips_coin():
    # Flips a coin: returns H or T
    choices = list('HT')
    random.shuffle(choices)
    return random.choice(choices)

def flips_until_hits(target):
    target = list(target)
    flips = []

    while True:
        result = flips_coin()
        flips.append(result)
        last_two_flips = flips[-2:]
        if len(flips) > 1 and last_two_flips == target:
            return flips

# Test Cases
HT_flipper_flips = []
HH_flipper_flips = []

#import pdb; pdb.set_trace()

# Run 10000 tests
for n in range(10000):
    HT_flipper_flips.append(len(flips_until_hits('HT')))
    HH_flipper_flips.append(len(flips_until_hits('HH')))

print('HT flipper AVG: %.2f' % (sum(HT_flipper_flips) / len(HT_flipper_flips)))
print('HH flipper AVG: %.2f' % (sum(HH_flipper_flips) / len(HH_flipper_flips)))

Python-Coin-Flip-Problem.md

From a comment by aws17576 on MetaFilter:

By the way, I wholeheartedly endorse Persi Diaconis's comment that probability is one area where even experts can easily be fooled. This was demonstrated to me in grad school when my advisor, addressing a roomful of mathematicians, posed this problem:

Person A flips a coin repeatedly, stopping the first time two heads in a row appear. Person B flips a coin repeatedly, stopping the first time a head and then a tail appear in a row. Who will flip the coin more times on average -- A, B, or is there no difference?

He let everyone think for a moment, then took a show of hands. Almost everyone got it wrong.