Determine the chance a streak of 6 HEADs or 6 TAILS appear in 100 flips, repeated 10000 times [closed]

Question

Here's the problem from the book Automate the boring stuff:

write a program to find out how often a streak of six heads or a streak of six tails comes up in a randomly generated list of heads and tails.

The #comments are a hint by the author. This program I created ran just fine but the chance of streak is surprisingly high to me: ~152% - 153%. So I'm wondering if I got the logic right? Any help will be greatly appreciated.

import random

def flip():
    random_num = random.randint(0, 1)
    if random_num == 1:
        return "H"
    else:
        return 'T'
            
numberOfStreaks = 0 #author wrote this line
for experimentNumber in range(10000): #author wrote this line
# Code that creates a list of 100 'heads' or 'tails' values.

    head_tail_str = ""
    side = flip() 
    head_tail_str += side
    for _ in range(99):
        prev_side = side
        side = flip()
        if side != prev_side:
            head_tail_str += f",{side}"
        else:
            head_tail_str += side

# Code that checks if there is a streak of 6 heads or tails in a row.

    head_tail_lst = head_tail_str.split(',')
    for item in head_tail_lst:
        if len(item) >= 6:
            numberOfStreaks += (int(len(item)) // 6)

print('Chance of streak: %s%%' % (numberOfStreaks / 100)) #author wrote this line

P.S. I've been learning Python for 1 month

Answer 1

Logical

            numberOfStreaks += (int(len(item)) // 6)

Does a streak of 12 H mean 2 streaks?

---

how often a streak of six heads or a streak of six tails comes up

Sounds like just numberOfStreaks to me, not sure why it's being suggested to compare to 100 in order to produce a percentage:

print('Chance of streak: %s%%' % (numberOfStreaks / 100)) #author wrote this line

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for experimentNumber in range(10000): #author wrote this line

The above suggests the code is designed to run multiple trials. For this to happen, it's important that each trial is independent, meaning state (values/data) does not bleed from one trial to another.

You'll see that's not happening if you run the script with this line instead:

for experimentNumber in range(1):

Structural

Would suggest using list instead of str to collect the flips, which more naturally expresses "a bunch of items".

It also helps to organize code by splitting up the two things you're doing: flipping 100 times and grouping together streaks.

# flip 100 times
flips = []
for _ in range(100):
    flips.append(flip())

# group together streaks:
first_flip, *rest_flips = flips
streaks = [[first_flip]]

for side in rest_flips:
    prev_streak = streaks[-1]  # [-1] returns the last item
    prev_side = prev_streak[-1]

    if side == prev_side:
        streak = prev_streak
    else:
        streak = []  # new streak
        streaks.append(streak)

    streak.append(side)

For "nicer" code

numberOfStreaks = 0 #author wrote this line

The convention in Python is underscore naming for variables, i.e. number_of_streaks.

---

In Python, 0 is "fasley", which means flip() can be:

    if random.randint(0, 1):
        return "H"  # when 1, "truthy"
    else:
        return "T"  # when 0, "falsey"

---

When grouping, can do all the flips together rather than the first_flip and rest_flips separately by handling the first iteration edge case:

streaks = []
for side in flips:
    prev_side = streaks and streaks[-1][-1]  # `[]` is also falsey

    if side == prev_side:
        streak = streaks[-1]
    else:
        streak = []
        streaks.append(streak)

    streak.append(side)

Leveling up

One of the reasons to split up the flipping from the grouping is that grouping is so generally useful, it's already available in the standard library as itertools.groupby:

import itertools as it

flips = [flip() for _ in range(100)]
streaks = [list(grp) for _, grp in it.groupby(flips)]