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Coin Flip Problem
import random
def flips_coin():
# Flips a coin: returns H or T
choices = list('HT')
return random.choice(choices)
def flips_until_hits(target):
target = list(target)
flips = []
while True:
result = flips_coin()
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):
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)))

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.

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