Monty Hall.ipynb

Kernel: Python 3 (system-wide)

Monty Hall Simulation

import random as rd

def run(V = False):
# create door scheme
    doors = [False, False, False]
# place car
    car = rd.randint(0,2)
    doors[car] = True
    if V: print(f'doors are {doors}')
# contestant chooses door
    firstChoice = rd.randint(0,2)
    if V: print(f'contestant chooses {firstChoice}')
# monty chooses a door to open
    possibleToReveal = [door for door in [0,1,2] if door not in [car, firstChoice]]
    montyOpens = possibleToReveal[rd.randint(0,len(possibleToReveal)-1)]
    if V: print(f'monty opens {montyOpens}')
# contestant chooses to switch or stay
    movement = ['switch', 'stay'][rd.randint(0,1)]
    if V: print('contestant chooses to ' + movement + ' so is at ', end='')
# contestant gets the new location
    possibleToSwitchTo = [door for door in [0,1,2] if door not in [montyOpens, firstChoice]][0]
    finalChoice = {'switch': possibleToSwitchTo, 'stay':firstChoice}[movement]
    if V: print(f'{finalChoice}')
# contestant gets their prize
    prize = doors[finalChoice]
    if V:
        if prize:
            print('contestant wins')
        else:
            print('contestant loses')
    return (movement, prize)

run('V')

doors are [False, True, False]
contestant chooses 0
monty opens 2
contestant chooses to switch so is at 1
contestant wins

('switch', True)

def run2(V = False):
# create door scheme
    doors = [False, False, False]
# place car
    car = rd.randint(0,2)
    doors[car] = True
    if V: print(f'doors are {doors}')
# contestant chooses door
    firstChoice = rd.randint(0,2)
    if V: print(f'contestant chooses {firstChoice}')
# monty chooses a door to open
    montysChoice = rd.randint(0,2)
    while montysChoice == firstChoice and montysChoice == car:
        montysChoice = rd.randint(0,2)
    montyOpens = montysChoice
    if V: print(f'monty opens {montyOpens}')
# contestant chooses to switch or stay
    movement = ['switch', 'stay'][rd.randint(0,1)]
    if V: print('contestant chooses to ' + movement + ' so is at ', end='')
# contestant gets the new location
    possibleToSwitchTo = [door for door in [0,1,2] if door not in [montyOpens, firstChoice]][0]
    finalChoice = {'switch': possibleToSwitchTo, 'stay':firstChoice}[movement]
    if V: print(f'{finalChoice}')
# contestant gets their prize
    prize = doors[finalChoice]
    if V:
        if prize:
            print('contestant wins')
        else:
            print('contestant loses')
    return (movement, prize)

def simulate(f, n):
    wonWhenSwitched = 0
    lostWhenSwitched = 0
    wonWhenStayed = 0
    lostWhenStayed = 0
    for _ in range(n):
        movement, prize = f()
        if movement == 'switch':
            if prize == 1:
                wonWhenSwitched += 1
            else:
                lostWhenSwitched += 1
        elif movement == 'stay':
            if prize == 1:
                wonWhenStayed += 1
            else:
                lostWhenStayed += 1
    print(f'Switch and win:  {round(wonWhenSwitched*100/(wonWhenSwitched+lostWhenSwitched), 3)} %')
    print(f'Switch and lose: {round(lostWhenSwitched*100/(wonWhenSwitched+lostWhenSwitched), 3)} %\n')
    print(f'Stay   and win:  {round(wonWhenStayed*100/(wonWhenStayed + lostWhenStayed), 3)} %')
    print(f'Stay   and lose: {round(lostWhenStayed*100/(wonWhenStayed + lostWhenStayed), 3)} %')

# where monty knows where the car is

simulate(run,1_000_000)

Switch and win:  66.662 %
Switch and lose: 33.338 %

Stay   and win:  33.36 %
Stay   and lose: 66.64 %

# where monty doesn't know where the car is

simulate(run2,1_000_000)

Switch and win:  33.285 %
Switch and lose: 66.715 %

Stay   and win:  33.452 %
Stay   and lose: 66.548 %