The Monty Hall problem is a brain teaser, there are several ways to explain the solution but none would be so convincing as a simple simulation.
Here is the one in Python for “Always Switch”
import numpy as np
import random#large sampling
sample = 1000000
#initialize doors and others
doors = ['car','goat','goat']
win = 0
lose = 0
for n in range(sample):
#shuffle every time
random.shuffle(doors)
# where is the car? zero index so add 1
c = doors.index('car')+1
# random select 1..3
i = random.randint(1,3)
#incease you want to know Monty opens? neither i or c
o = [v for v in [1,2,3]if v not in [i,c]]
#always switch, so if original selection is car
#then it's a lose
if(i == c):
lose += 1
else:
win +=1
##print the results of always switch##
print("Wins:{}, Losses:{}, Prob:{:.4f}".format(win, lose, win/(win+lose)))[out] Wins:666698, Losses:333302, Prob:0.6667
That’s all folks!
PS: Image courtesy https://en.wikipedia.org/wiki/Monty_Hall_problem
