e01_monty_hall_experiments.sagews

2+3 == 7

False

#2+3 == 7
5 == 5

True

[1..100]

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]

for i in [5,6,7]:
    print 2*i +17

27 29 31

n = 1000000
count0 = 0.0
count1 = 0.0
count2 = 0.0
for i in [1..n]:
    guess = randint(0,2)
    if guess == 0: #write a comment here
        count0 = count0 + 1
    if guess == 1: #write a comment here
        count1 = count1 + 1
    if guess == 2: #write a comment here
        count2 = count2 + 1
print("The percentage of 0s, 1s, 2s is {}, {}, {}").format(count0/n,count1/n,count2/n)

The percentage of 0s, 1s, 2s is 0.333392000000000, 0.333392000000000, 0.333216000000000

L=[0,1,2]
L.remove(1)
L

[0, 2]

L=[5,6,7]
L[0]
L[2]

5 7

L

[5, 6, 7]

9 in L

False

5 in L

True

doors=[0,2]
doors.remove(2)
doors
doors[0]

[0] 0

#represent the 3 doors with the Integers 0, 1 and 2
# let Sage choose the location of the car by randomly choosing one of 0,1 or 2
car = randint(0,2)
guess1 = 2
#represent the doors with list [0,1,2], remove the
doors = [0,1,2]
doors.remove(guess1)
if car in doors:
    doors.remove(car)
    monty = doors[0]
else:
    monty = doors[randint(0,1)]

print("Monty opens door {}").format(monty)

Monty opens door 1

guess2 = 0
if car == guess2:
    print("You win! You get the car")
else:
    print("You lose!")

You win! You get the car

#here's a version that makes the contestants' guess *randomly*

#represent the 3 doors with the Integers 0, 1 and 2
# let Sage choose the location of the car by randomly choosing one of 0,1 or 2

car = randint(0,2)
#let's print where the car is to see how things are looking
print("The car is really behind door {}".format(car))

guess1 = randint(0,2)
#let's print the guess to see how things are looking
print("I guess the car is behind door {}".format(guess1))

#represent the doors with list [0,1,2], remove the doors with the contestant's guess and the one with the car
doors = [0,1,2]
doors.remove(guess1)
#use the variable *monty* to represent the door that monty opnes
if car in doors:
    doors.remove(car)
    monty = doors[0]
else:
    monty = doors[randint(0,1)]

print("Monty opens door {}").format(monty)

#here is where we implement the strategy
#Strategy 1 was to *not* switch the guess - so we stick with guess1
guess2 = guess1
if car == guess2:
    print("You win! You get the car")
else:
    print("You lose!")

The car is really behind door 2 I guess the car is behind door 1 Monty opens door 0 You lose!

#now lets try Strategy 2
#here's a version that makes the contestants' guess *randomly*

#represent the 3 doors with the Integers 0, 1 and 2
# let Sage choose the location of the car by randomly choosing one of 0,1 or 2

car = randint(0,2)
#let's print where the car is to see how things are looking
print("The car is really behind door {}".format(car))

guess1 = randint(0,2)
#let's print the guess to see how things are looking
print("I guess the car is behind door {}".format(guess1))

#represent the doors with list [0,1,2], remove the doors with the contestant's guess and the one with the car
doors = [0,1,2]
doors.remove(guess1)
#use the variable *monty* to represent the door that monty opnes
if car in doors:
    doors.remove(car)
    monty = doors[0]
else:
    monty = doors[randint(0,1)]

print("Monty opens door {}").format(monty)

#here is where we implement the strategy
#Strategy 2 was to *switch* the guess - so we stick with guess1
doors = [0,1,2]
doors.remove(guess1)
doors.remove(monty)
guess2 = doors[0]
#let's print the guess to make sure this does what we want
print("I switch my guess to door {}".format(guess2))
if car == guess2:
    print("You win! You get the car")
else:
    print("You lose!")

The car is really behind door 1 I guess the car is behind door 2 Monty opens door 0 I switch my guess to door 1 You win! You get the car

#now let's try Strategy #1 n times and see how we do in percentage
#we remove all print statements as we don't want to print them possible thousands of times!

n = 1000000

#we'll define a counter *count* to record the number of wins
count = 0

#we need a *loop* in order to get the n repetitions
for i in [1..n]:
    #represent the 3 doors with the Integers 0, 1 and 2
    # let Sage choose the location of the car by randomly choosing one of 0,1 or 2



    car = randint(0,2)

    guess1 = randint(0,2)

    #represent the doors with list [0,1,2], remove the doors with the contestant's guess and the one with the car
    doors = [0,1,2]
    doors.remove(guess1)
    #use the variable *monty* to represent the door that monty opnes
    if car in doors:
        doors.remove(car)
        monty = doors[0]
    else:
        monty = doors[randint(0,1)]

    #here is where we implement the strategy
    #Strategy 1 was to *not* switch the guess - so we stick with guess1
    guess2 = guess1
    if car == guess2:
        count = count + 1

print("The percentage of success using Strategy #1 with {} trials is {}".format(n,count/n*100.0))

The percentage of success using Strategy #1 with 1000000 trials is 33.3023000000000

#now let's try Strategy #2 n times and see how we do in percentage
#we remove all print statements as we don't want to print them possible thousands of times!

n = 1000000

#we'll define a counter *count* to record the number of wins
count = 0

#we need a *loop* in order to get the n repetitions
for i in [1..n]:
    #represent the 3 doors with the Integers 0, 1 and 2
    # let Sage choose the location of the car by randomly choosing one of 0,1 or 2



    car = randint(0,2)

    guess1 = randint(0,2)

    #represent the doors with list [0,1,2], remove the doors with the contestant's guess and the one with the car
    doors = [0,1,2]
    doors.remove(guess1)
    #use the variable *monty* to represent the door that monty opnes
    if car in doors:
        doors.remove(car)
        monty = doors[0]
    else:
        monty = doors[randint(0,1)]

    #here is where we implement the strategy
    #Strategy 2 was to *switch* the guess - so we stick with guess1
    doors = [0,1,2]
    doors.remove(guess1)
    doors.remove(monty)
    guess2 = doors[0]

    if car == guess2:
        count = count + 1

print("The percentage of success using Strategy #1 with {} trials is {}".format(n,count/n*100.0))

The percentage of success using Strategy #1 with 1000000 trials is 66.6084000000000

#Strategy 3
#place the car randomly behind one of 3 doors
car = randint(0,2)
#we assume the contestant always starts by guessing the car is behind door 0
#monty will open one of door 1 or 2
#if the car is behind door 1, monty opens door 2
#if the car is behind door 2, monty opens door 1
#if the car is behind door 0, monty randomly selects one of doors 1 or 2
#if monty opens door 1 we switch our guess,
#if he opens door 2 we stick with door 0 (this was a TYPO, the worksheet strategy is really original strategy 2)

if car == 0:
    monty = randint(1,2)
    if monty == 1:
        guess = 2 #note: we fail
    if monty == 2:
        guess = 0 #note: we win
if car == 1:
    guess = 0 #note: we fail
if car == 2:
    guess = 2 #note: we win
if car == guess:
    print "you win!"

you win!

#repeat this experiment n times, find the ratio of successes
n=1000
successes = 0
for i in [1..n]:
    car = randint(0,2)
    if car == 0:
        monty = randint(1,2)
        if monty == 1:
            guess = 2 #note: we fail
        if monty == 2:
            guess = 0 #note: we win
    if car == 1:
        guess = 0 #note: we fail
    if car == 2:
        guess = 2 #note: we win
    if car == guess:
        successes = successes+1
print successes/n*100.0

51.2000000000000