A collection of simple simulations in Python
Python makes it very easy to create simple simulations to simulate complex processes. There is usually a math solution but that can be hard to remember.
In the spirit of Raymond Hettinger's Modern Python LiveLessons: Big Ideas and Little Code in Python course. We will explore some basic simulation.
Streak Length History of an American Roulette Wheel
The American Roulette has 18 black and red pockets plus TWO green pockets. Making it a total of 38 pockets.
To simulate this whell we just need one line of Python code. In the following code the roulette wheel is spun 1,000 times
from random import *
from collections import *
Counter(choices(['black', 'red', 'green'], weights=[18,18,2], k=1000))
The hit counts are below. Red was hit 476 times (~48%). The two greens were only hit 53 times (5.3%) which makes sense since 2/38 = 5.2%
Now, how often do we hit a streak of any color? The following code does just that:
# spin the wheel 100,000 times
spins = choices(['black', 'red', 'green'], weights=[18,18,2], k=100_000)
def streak_lengths(spins):
streaks = []
current = spins[0]
length = 1
for s in spins[1:]:
if s == current:
length += 1
else:
streaks.append((current, length))
current = s
length = 1
streaks.append((current, length))
return streaks
streaks = streak_lengths(spins)
# we are only interested in streaks of longer than 4 spins
streaks_counter = Counter([s[1] for s in streaks if s[1] > 4])
print(streaks_counter)
The output is:
As you can see very long streaks are indeed possible albeit very rarely.