**Python Puzzles**

The following puzzle was taken from the book

Of Course! The Greatest Collection Of Riddles & Brain Teasers For Expanding Your Mind by Zack Guido

Your friend has a coin and asks you if you want to play a game:

“I will flip this coin until the number of heads flipped is equal to the number of tails flipped. Then I will give you a dollar for each time I flipped the coin.”

What are the chances that you play this game with your friend once and he pays you exactly eight dollars?

I first run the simulation 10,000 times (inner loop)

and determine the number of iterations where the heads and tails

match exactly on the 8th flip.

I then run the above simulation another 10,000 times (outer loop) and take

the average of these 10,000 averages.

According to the book, there is a 3.9% chance that you will play this game one time.

When running multiple times, I receive an average anywhere from 3.5% to 4.5%.

Here are the results of the print statement after running the code.

The Average is 3.97%

The Minimum is 0.00%

The Maximum is 9.52%

The Standard Deviation is 0.56%

```
import numpy as np
exactly_8 = []
result = []
for _ in range(10_000):
for _ in range(10_000):
arr = np.random.randint(2, size=9)
heads = []
tails = []
for x in arr:
heads.append(1) if x == 1 else tails.append(1)
if len(heads) == len(tails) or len(heads) + len(tails) == 9:
result.append(len(heads) + len(tails))
break
exactly_8.append(result.count(8)/len(result))
arr = np.array(exactly_8)
print('The Average is ' + '{0:.2%}'.format(np.average(arr)))
print('The Minimum is ' + '{0:.2%}'.format(np.min(arr)))
print('The Maximum is ' + '{0:.2%}'.format(np.max(arr)))
print('The Standard Deviation is ' + '{0:.2%}'.format(np.std(arr)))
```