Monty Hall Problem Simulation

monty.py

## Monty Hall Problem
## https://en.wikipedia.org/wiki/Monty_Hall_problem
##
## A simulation intended to prove the Monty Hall Solution wrong
## (that switching selection after one door is revealed increases
## the odd from 1/3 to 2/3), ended up proving it right.
##
## Result of running run(1000) 100 times:  0.67(+-)0.02
## 

import random, statistics

def monty():
  car = random.choice([0,1,2]) 
  pick = random.choice([0,1,2])
  
  no_car = [0,1,2]
  no_car.remove(car) 
  
  if car==pick: ## if car==pick, randomly remove one of the other 2
     remove= random.choice( no_car ) 
  else:         ## Otherwise, remove the one neither car nor pick
     remove = no_car
     remove.remove(pick)
     remove=remove[0]
  
  remain = [0,1,2]
  remain.remove(remove)  ## The remaining 2 after one door is revealed
  
  switchpick = remain    
  switchpick.remove(pick)   
        
  return [car, pick, remove, switchpick[0]]

def run(n=1000):
  runs = [ monty() for i in range(n) ]
  switched = [ (car==switchpick and 1) or 0 for car,pick,remove,switchpick in runs ]
  unswitched = [ (car==pick and 1) or 0 for car,pick,remove,switchpick in runs ]
  #return sum(unswitched)/n 
  return sum(switched)/n 
  
## Test run(1000) k times 
k = 100
result = [ run() for i in range(k)]  
print( "{:.2f}(+-){:.2f}".format(sum(result)/k, statistics.stdev( result) ))