# The Monty Hall Problem

I was watching MythBusters and they visited this problem which at Seneca we discussed briefly as well (I might have done this one before but thought I’d repost it anyway):

1. There are 3 doors, 2 are losers and 1 is a winner
2. You pick a door (2/3 chance it’s a loser)
3. They show you the other loser door (leaving the winner door [1/3 chance] and the loser door [2/3 chance])
4. You decide to switch your door (since it was 2/3 likely you originally chose a losing door and they took the other losing door away, switching increases your odds since the other door is likely to be the winner door)
5. You win! (still a small chance of losing though)

```\$ python monty.py 0 100 1

('Doors:', {1: 'win', 2: 'lose', 3: 'lose'})
('Pick:', 1, 'win')
('Show:', 2, 'lose')
('Final:', 1, 'win')

('Doors:', {1: 'lose', 2: 'lose', 3: 'win'})
('Pick:', 2, 'lose')
('Show:', 1, 'lose')
('Final:', 2, 'lose')

('Doors:', {1: 'lose', 2: 'lose', 3: 'win'})
('Pick:', 1, 'lose')
('Show:', 2, 'lose')
('Final:', 1, 'lose')

('Wins:', 32, '/', 100, '=', 0.32)

\$ python monty.py 1 100 1

('Doors:', {1: 'lose', 2: 'win', 3: 'lose'})
('Pick:', 2, 'win')
('Show:', 1, 'lose')
('Switching:', 2, 'to', 3)
('Final:', 3, 'lose')

('Doors:', {1: 'lose', 2: 'win', 3: 'lose'})
('Pick:', 3, 'lose')
('Show:', 1, 'lose')
('Switching:', 3, 'to', 2)
('Final:', 2, 'win')

('Doors:', {1: 'lose', 2: 'win', 3: 'lose'})
('Pick:', 1, 'lose')
('Show:', 3, 'lose')
('Switching:', 1, 'to', 2)
('Final:', 2, 'win')

('Wins:', 74, '/', 100, '=', 0.74)
```
```import random
import sys
try:
switch = int(sys.argv[1])
except:
switch = 0
try:
rounds = int(sys.argv[2])
except:
rounds = 0
try:
debug = int(sys.argv[3])
except:
debug = 0
wins = 0
for x in range(0, rounds):
doors = ["lose", "lose", "win"]
random.shuffle(doors)
doors = {1:doors[0], 2:doors[1], 3:doors[2]}
if (debug != 0):
print("Doors:", doors)
pick = random.randint(1, 3)
if (debug != 0):
print("Pick:", pick, doors[pick])
show = 1
for k in doors.keys():
if ((k != pick) and (doors[k] == "lose")):
show = k
break
if (debug != 0):
print("Show:", show, doors[show])
if (switch != 0):
for k in doors.keys():
if ((k != pick) and (k != show)):
other = k
break
print("Switching:", pick, "to", other)
pick = other
print("Final:", pick, doors[pick])
if (doors[pick] != "lose"):
wins += 1
if (debug != 0):
print("")
print("")
print("Wins:", wins, "/", rounds, "=", float(wins) / float(rounds))

```

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