Gradient Dissents

Coin Flip Probability with Python

Jun 18, 2018 | 3 minutes read
Share this:

I’m writing up my dissertation…but occasionally I need a distraction. Don’t get me wrong, I find studying hate speech very fascinating, but in all honesty, it gets to be a bit much sometimes. The world can be a depressing place. Plus, it’s a dissertation; distractions are welcome in any flavor.

Today my distraction came in the form of a Tweet by David Robinson demonstrating how flipping a coin and getting a heads and then another heads takes 6 flips on average while a heads then a tails only takes 4.

He did this using tidyverse functions and then using base-R matrix operations. Well, I wanted to create the Python version because of said dissertation. I did so by creating a set of functions.

The first is simply a function to simulate flipping a fair coin…

import numpy as np

def flip_coin():
    """Simulate flipping a coin.
        "H" for heads/ "T" for tails.
    flip = np.random.binomial(1, .5, 1)
    if flip[0] == 1:
        side = "H"
        side = "T"
    return side

Then I need a function to flip the coin multiple times and to stop only when a certain sequence of sides were met. In other words, stop when two heads were flipped in a row. From this, I want the number of times it took to achieve this sequence to be returned.

def flip_condition(stop_condition=['H', 'T'], print_opt=False):
    """Flip coin until flip pattern is met.
    stop_condition: list
        The sequence of flips to be matched before flipping stops.
    print_opt: bool
        Option to print the sequence of flips.
        The number of flips it took to match the pattern.
    flip_list = []
    current_index = 0
    current_condition = None
    while current_condition != stop_condition:
        if len(flip_list) >= len(stop_condition):
            current_condition = [flip_list[i] for i in range(current_index - len(stop_condition) +1 , current_index + 1)]
        current_index +=1
    if print_opt:
    return current_index 

This also includes an option to print the sequence (in case you want to check my programming…I would 😜). And then I just run it many times and take the average for both conditions.

mean_ht = np.mean([flip_condition(['H', 'T']) for i in range(10000)])
mean_hh = np.mean([flip_condition(['H','H']) for i in range(10000)])

print("Average # of flips to achieve heads and then heads again: {}".format(mean_hh))
print("Average # of flips to achieve heads and then tails: {}".format(mean_ht))

# Average # of flips to achieve heads and then heads again: 6.0081
# Average # of flips to achieve heads and then tails: 3.9829

Looks like probability holds up in Python! Oh, but I also created the function to capture any pattern. How about heads, tails, heads?

np.mean([flip_condition(['H', 'T', 'H']) for i in range(10000)])

# 9.9231

or heads, heads, heads

np.mean([flip_condition(['H', 'H', 'H']) for i in range(10000)])

# 14.1544

Well that was neat! 🦖🦕

If you want to play around with the code, I’ve posted in this notebook here

comments powered by Disqus