Python simulation of Monty Problem

2. Monty Problem
 Problem originated from show
“Lets make a deal”*
 3 doors, 1 contains a price
($1000)
 Price place at random
 Ex: D1
 Player picks a door
 Ex: D1
 Host opens a door that
doesn’t have the price
 Ex: D3
 Should player switch to the
other door?
*https://en.wikipedia.org/wiki/Monty_Hall_problem
D1 D2 D3
D1 or D2 ?

3. “Causality, there’s no escape from it”

4. Simulating Monty Problem
in Python
 Price placed at
random in one of 3
doors
 1000 trials run
 Each door has
probability 1/3 of
having the price
 Each door has
price ~333 times
np.random.seed()
doorPr = int(np.floor(np.random.uniform(1, 4))) # door where price is
doorPrice.append(doorPr)

5. Simulating Monty Problem
in Python
 Player 1 picks door at
random and never switches
to the other door
 Player 2 also picks door at
random but always switches
to the other door after host
shows empty door
 Who is more likely to win?

6. Simulating Monty Problem
in Python
 Players 2 wins
twice as much!

7. Python Code
import numpy as np
from matplotlib import pyplot as plt
trials = 1000
doorPrice = []
doorPlayer1 = []
doorPlayer2 = []
doorPlayer2b = []
doorOther = []
doorOther3 = []

8. Python Code
def getWinnings(doorPrice,doorPlayer):
w = 0
for price, player in zip(doorPrice,doorPlayer):
if price == player:
w += 1
return w

9. Python Code
def switchDoor2(doorDict):
# choose door that has a 0 value (wasn't chosen)
for key,value in doorDict.iteritems():
if value ==0:
return int(key[1])

10. Python Code
for t in range(trials):
np.random.seed()
doorPr = int(np.floor(np.random.uniform(1, 4))) # door where price is
doorPrice.append(doorPr)
# player 1
doorP1 = int(np.floor(np.random.uniform(1, 4))) # door for player 1
doorPlayer1.append(doorP1)
doorList = [doorPr, doorP1]
doorDict = {'d1':0,'d2':0,'d3':0}

11. Python Code
for door in doorList:
key = 'd' + str(door)
doorDict[key]+=1 # Add 1 to value in dictionary
# whenever a door is chosen
other2 = switchDoor2(doorDict) # host opens door different
from
# door with prize and chosen by player 1

12. Python Code
# player 2
doorP2 = int(np.floor(np.random.uniform(1, 4)))
doorPlayer2.append(doorP2)
doorList = [doorPr, doorP2]
doorDict = {'d1': 0, 'd2': 0, 'd3': 0}
for door in doorList:
key = 'd' + str(door)
doorDict[key] += 1

13. Python Code
other3 = switchDoor2(doorDict)
key = 'd'+str(other3)
del doorDict[key] # door no longer available since it was open
for key in doorDict.keys():
keyP2 = 'd' + str(doorP2)
if keyP2 != key:
switch = int(key[1])
doorOther3.append(other3)
doorPlayer2b.append(switch)