# The Monty Hall Problem in Python

Again, this is another coding exercise in Dream.In.Code. Well, it is actually a challenge but since my submission pales compared to the others, I don't prefer to call it as one.

What is the **Monty Hall Problem**?

*Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?*

Read more here:

http://www.dreamincode.net/forums/topic/292496-prove-the-monty-hall-problem-via-simulation/

http://en.wikipedia.org/wiki/Monty_Hall_problem

Basically, you need to prove that switching doors when asked to switch will improve your chances by 2/3 as opposed to the 1/3 chance if you don't switch doors.

Here's what I cooked up:

*Door Creation*

```
def addDoors():
picker = randint(0,1)
if picker == 1:
door1,door2,door3 = "dragon","goat","goat"
else:
door1 = "goat"
picker = randint(0,1)
if picker == 1:
door2,door3 = "dragon","goat"
else:
door2,door3 = "goat","dragon"
return [door1,door2,door3]
```

*Goat Door Opener*

```
def openGoatDoor(doors):
door = ""
while door != "goat":
doorNumber = randint(0,2)
door = doors[doorNumber]
return doorNumber
```

*The Monty Hall Simulation*

```
def montyhall(doorNumber,switchOk):
doors = addDoors()
goatDoor = addDoors()
while goatDoor == doorNumber:
goatDoor = openGoatDoor(doors)
if switchOk == "yes":
doorNumber = [y for y in range(2) if y not in [doorNumber,goatDoor]]
return doors[doorNumber[0]]
else:
return doors[doorNumber]
```

*The Tester*

```
def testMontyHall(playTimes,switch):
wondragon,wonGoat = 0,0
for i in range(playTimes):
prize = montyhall(randint(0,2),switch)
if prize == "dragon":
wondragon += 1
else:
wonGoat += 1
print "Dragons:",wondragon
print "Goat:",wonGoat
```

*The Results*

>>> testMontyHall(1000000,"no")

Dragons: 332961

Goat: 667039

>>> testMontyHall(1000000,"yes")

Dragons: 666757

Goat: 333243

And this concludes The Monty Hall show. Hope you enjoyed it.

#### Written by Julius Santos

#### Related protips

#### 1 Response

Here's mine, yours is a bit fancier!

Functions:

```
#monty_hall.py
def gen_doors():
doors = [0,1,2]
car = random.randrange(3)
doors[car] = "Car"
goats = list(range(3))
del goats[car]
for i in goats:
doors[i] = "Goat"
return doors
def random_play(doors = ["Goat","Car","Goat"], switch = True):
goats = []
[goats.append(i) for i in range(3) if doors[i] == "Goat"]
pick = random.randrange(3)
if switch == True:
if pick in goats:
return "Car"
else: return "Goat"
else:
if pick in goats:
return "Goat"
else: return "Car"
```

```
#sim.py
import monty_hall
plays = 100000
# With Switch:
n_goats = 0
n_cars = 0
for i in range(plays):
if monty_hall.random_play(monty_hall.gen_doors(), True) == "Goat": n_goats += 1
else: n_cars += 1
print("With Switching:\nGoats: ", n_goats, "\n", "Cars: ", n_cars, "\n")
n_goats = 0
n_cars = 0
# Without Switch:
for i in range(plays):
if monty_hall.random_play(monty_hall.gen_doors(), False) == "Goat": n_goats +=1
else: n_cars +=1
print("Without Switching:\nGoats: ", n_goats, "\n", "Cars: ", n_cars)
```

[Out]

With Switching:

Goats: 33210

Cars: 66790

Without Switching:

Goats: 66812

Cars: 33188