Hacker Statistics

We will use hacker statistics to calculate the chances of winning a bet. Use random number generators, loops, and Matplotlib to gain a competitive edge!Imagine you are walking the Empire State Building to Data Camp Head Quarters and you are playing a game with a friend. In the Empire State Building bet, your next move depends on the number of eyes you throw with the dice. We can perfectly code this with an if-elif-else construct! Falling down means you have to start again from step 0.

Betting: you will reach step 60

1. If dice is 1 or 2, you go one step down.
2. if dice is 3, 4 or 5, you go one step up.
3. If you throw a 6, you throw the dice again and will walk up the resulting number of steps.
4. You have 0.1% chance of faling down the stairs.
5. Can't go below step 0.
6. The number of eyes is the number of steps you go up.

What is the chance that you will win this bet?

Con toss

import numpy as np
np.random.seed(123)
coin =np.random.randint(0,2)
if coin == 0:
    print('head')
else:
    print('tails')

head

dict ={'0':'head', '1':'tails'}
toss= [np.random.randint(0,2) for i in range(100)]

[dict[str(coin)] for  coin in [np.random.randint(0,2) for i in range(100)]];

Roll the dice

# Import numpy and set seed
import numpy as np
np.random.seed(123)

# Starting step
step = 50

# Roll the dice
dice = np.random.randint(1,7)

# Finish the control construct
if dice <= 2 :
    step = step - 1
elif dice<=5 :
    step =step + 1
else :
    step = step + np.random.randint(1,7)

# Print out dice and step
print(dice)
print(step)

6
53

Random Walk

import numpy as np
# Initialize random_walk
random_walk=[0]

# Complete the ___
for x in range(100) :
    # Set step: last element in random_walk
    step=random_walk[-1]

    # Roll the dice
    dice = np.random.randint(1,7)

    # Determine next step
    if dice <= 2:
        step = step - 1
    elif dice <= 5:
        step = step + 1
    else:
        step = step + np.random.randint(1,7)

    # append next_step to random_walk
    random_walk.append(step)

# Print random_walk
print(random_walk)

[0, 1, 2, 1, 2, 3, 4, 3, 2, 1, 0, -1, -2, -3, -4, -3, 2, 1, 0, 1, 0, 1, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 8, 7, 11, 12, 11, 12, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 29, 30, 34, 35, 34, 35, 36, 35, 36, 37, 39, 40, 41, 40, 39, 40, 41, 40, 39, 40, 41, 43, 42, 41, 42, 41, 42, 43, 44, 46, 45, 46, 47, 48, 49, 50, 49, 48, 49, 48, 49, 50, 49, 52, 53, 54, 55, 54, 55, 56, 60]

How low can you go?

# Initialize random_walk
random_walk = [0]

for x in range(100) :
    step = random_walk[-1]
    dice = np.random.randint(1,7)

    if dice <= 2:
        # Replace below: use max to make sure step can't go below 0
        step = max(0,step - 1)
    elif dice <= 5:
        step = step + 1
    else:
        step = step + np.random.randint(1,7)

    random_walk.append(step)

print(random_walk)

[0, 0, 0, 2, 1, 2, 4, 5, 6, 11, 10, 11, 12, 13, 14, 15, 14, 19, 20, 21, 22, 21, 20, 19, 18, 17, 18, 19, 20, 26, 25, 24, 23, 24, 25, 26, 25, 26, 27, 26, 31, 32, 31, 30, 29, 28, 29, 28, 27, 29, 30, 33, 34, 36, 37, 38, 39, 38, 37, 38, 39, 40, 41, 40, 41, 42, 43, 46, 47, 48, 47, 48, 47, 48, 49, 50, 54, 53, 52, 53, 54, 55, 54, 55, 54, 55, 57, 62, 61, 62, 63, 64, 65, 66, 67, 66, 67, 68, 69, 71, 73]

Visualize the walk

# Initialization
random_walk = [0]

for x in range(10) :
    step = random_walk[-1]
    dice = np.random.randint(1,7)

    if dice <= 2:
        step = max(0, step - 1)
    elif dice <= 5:
        step = step + 1
    else:
        step = step + np.random.randint(1,7)

    random_walk.append(step)

# Import matplotlib.pyplot as plt
import matplotlib.pyplot as plt

# Plot random_walk
plt.plot(random_walk)
# Show the plot
plt.show()

Simulate multiple walks

# Initialize all_walks (don't change this line)
all_walks = []

# Simulate random walk 10 times
for i in range(10) :

    # Code from before
    random_walk = [0]
    for x in range(100) :
        step = random_walk[-1]
        dice = np.random.randint(1,7)

        if dice <= 2:
            step = max(0, step - 1)
        elif dice <= 5:
            step = step + 1
        else:
            step = step + np.random.randint(1,7)
        random_walk.append(step)

    # Append random_walk to all_walks
    all_walks.append(random_walk)

# Print all_walks
print(all_walks)

[[0, 0, 1, 0, 1, 2, 4, 3, 2, 3, 4, 3, 5, 6, 7, 8, 9, 10, 11, 10, 11, 12, 17, 18, 17, 16, 15, 14, 15, 16, 17, 22, 23, 22, 23, 24, 25, 26, 27, 28, 27, 26, 27, 26, 32, 31, 32, 31, 32, 31, 32, 36, 40, 42, 44, 43, 44, 46, 45, 51, 52, 54, 55, 54, 55, 56, 57, 56, 57, 58, 59, 61, 60, 59, 60, 66, 71, 70, 69, 73, 74, 75, 76, 78, 77, 78, 77, 78, 77, 76, 82, 81, 82, 83, 84, 85, 86, 87, 88, 89, 88], [0, 1, 0, 0, 1, 0, 1, 0, 1, 2, 6, 7, 6, 12, 11, 10, 11, 10, 9, 10, 9, 13, 12, 13, 12, 13, 12, 13, 15, 14, 13, 12, 13, 12, 17, 18, 19, 18, 17, 18, 17, 18, 17, 22, 23, 22, 21, 20, 19, 20, 21, 25, 31, 32, 33, 34, 35, 34, 35, 37, 38, 39, 40, 39, 38, 39, 38, 39, 40, 41, 40, 41, 42, 43, 42, 41, 42, 43, 48, 49, 50, 55, 54, 55, 54, 55, 56, 57, 58, 57, 63, 62, 63, 62, 61, 62, 66, 67, 68, 69, 70], [0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 6, 7, 8, 11, 10, 11, 10, 11, 14, 15, 16, 17, 16, 15, 18, 19, 20, 21, 20, 19, 20, 23, 24, 29, 30, 29, 30, 29, 30, 29, 35, 34, 33, 34, 36, 35, 34, 33, 34, 35, 36, 37, 41, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 57, 56, 57, 58, 57, 63, 62, 63, 64, 63, 62, 63, 62, 61, 67, 66, 65, 66, 67, 66, 65, 64, 63, 64, 70, 71, 74, 75, 81, 82, 83, 89], [0, 0, 6, 5, 6, 7, 8, 7, 13, 14, 13, 14, 13, 14, 13, 14, 13, 14, 18, 19, 21, 20, 21, 20, 19, 20, 19, 20, 19, 23, 27, 26, 25, 24, 25, 26, 30, 31, 32, 36, 35, 34, 33, 34, 35, 37, 36, 35, 36, 37, 39, 42, 47, 48, 47, 48, 49, 50, 51, 52, 51, 52, 53, 59, 58, 63, 62, 66, 65, 69, 68, 71, 72, 71, 72, 78, 77, 76, 75, 79, 78, 77, 78, 79, 78, 79, 80, 81, 82, 81, 80, 79, 80, 79, 78, 82, 83, 85, 89, 95, 94], [0, 0, 1, 2, 3, 2, 3, 2, 3, 4, 3, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 18, 17, 20, 21, 20, 19, 20, 21, 22, 21, 20, 19, 18, 19, 20, 21, 22, 23, 24, 25, 24, 25, 26, 28, 27, 28, 29, 32, 34, 35, 34, 33, 32, 31, 30, 31, 30, 31, 33, 34, 35, 34, 35, 34, 33, 34, 33, 32, 31, 32, 31, 30, 31, 32, 33, 35, 36, 37, 36, 35, 36, 42, 41, 42, 43, 48, 47, 48, 47, 48, 49, 48, 49, 50, 56, 57, 58, 59, 58], [0, 2, 3, 4, 5, 4, 5, 6, 7, 8, 7, 8, 7, 8, 9, 8, 9, 13, 14, 17, 18, 22, 23, 22, 23, 24, 23, 22, 27, 28, 29, 28, 27, 28, 29, 30, 29, 33, 32, 33, 34, 35, 36, 37, 38, 39, 38, 37, 36, 37, 38, 42, 43, 42, 43, 44, 43, 49, 50, 51, 52, 51, 52, 53, 56, 55, 56, 55, 54, 53, 54, 55, 57, 58, 59, 63, 64, 63, 62, 63, 64, 63, 62, 63, 64, 65, 64, 63, 64, 65, 66, 65, 66, 67, 66, 65, 64, 65, 66, 67, 68], [0, 1, 6, 10, 9, 10, 9, 8, 7, 8, 7, 8, 9, 8, 12, 13, 12, 13, 12, 11, 12, 11, 15, 16, 17, 18, 19, 20, 19, 20, 21, 22, 23, 24, 23, 28, 29, 30, 29, 30, 29, 30, 31, 30, 31, 36, 37, 38, 37, 38, 39, 40, 39, 40, 39, 40, 41, 40, 39, 38, 39, 40, 39, 38, 37, 38, 42, 43, 44, 45, 46, 47, 46, 47, 48, 47, 48, 53, 54, 53, 52, 53, 52, 51, 50, 54, 55, 56, 57, 56, 57, 58, 59, 60, 61, 60, 59, 62, 61, 60, 59], [0, 0, 1, 7, 8, 7, 8, 9, 8, 7, 8, 9, 10, 9, 13, 14, 13, 15, 16, 15, 16, 17, 18, 19, 20, 21, 20, 19, 20, 21, 20, 21, 22, 21, 20, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 31, 32, 33, 34, 35, 36, 35, 34, 40, 41, 42, 41, 40, 39, 43, 44, 48, 47, 53, 54, 55, 59, 60, 59, 58, 59, 60, 61, 62, 61, 67, 68, 67, 71, 72, 71, 72, 71, 77, 83, 84, 83, 84, 85, 86, 87, 88, 87, 90, 89, 91, 92, 98, 97, 98], [0, 1, 0, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16, 15, 14, 13, 14, 13, 17, 16, 15, 16, 18, 19, 24, 23, 24, 25, 29, 28, 29, 30, 29, 28, 29, 30, 31, 30, 29, 28, 29, 28, 27, 28, 27, 26, 25, 26, 27, 26, 25, 24, 25, 26, 27, 26, 25, 26, 27, 28, 29, 28, 29, 28, 29, 30, 31, 32, 33, 38, 43, 42, 43, 44, 43, 44, 50, 49, 50, 49, 50, 49, 50, 51, 52, 51, 50, 51, 52, 53], [0, 0, 0, 0, 2, 3, 4, 3, 2, 1, 2, 3, 4, 3, 2, 3, 6, 11, 14, 15, 16, 22, 23, 24, 25, 24, 26, 31, 32, 33, 34, 35, 36, 37, 36, 37, 38, 39, 40, 41, 43, 47, 48, 49, 50, 51, 55, 60, 59, 58, 57, 56, 59, 60, 61, 62, 61, 60, 63, 64, 63, 62, 61, 62, 63, 64, 65, 64, 65, 64, 65, 66, 65, 66, 67, 68, 69, 70, 71, 72, 71, 70, 71, 72, 75, 76, 75, 74, 75, 76, 77, 82, 81, 80, 79, 78, 77, 76, 77, 76, 75]]

Visualize all walks

# initialize and populate all_walks
all_walks = []
for i in range(10) :
    random_walk = [0]
    for x in range(100) :
        step = random_walk[-1]
        dice = np.random.randint(1,7)
        if dice <= 2:
            step = max(0, step - 1)
        elif dice <= 5:
            step = step + 1
        else:
            step = step + np.random.randint(1,7)
        random_walk.append(step)
    all_walks.append(random_walk)

# Convert all_walks to Numpy array: np_aw
np_aw=np.array(all_walks)

# Plot np_aw and show
plt.plot(np_aw)
plt.show()
# Clear the figure
plt.clf()

# Transpose np_aw: np_aw_t
np_aw_t=np.transpose(np_aw)

# Plot np_aw_t and show
plt.plot(np_aw_t)
plt.show()

Implement clumsiness

You're a bit clumsy and you have a 0.1% chance of falling down.

# Simulate random walk 250 times
all_walks = []
for i in range(500) :
    random_walk = [0]
    for x in range(100) :
        step = random_walk[-1]
        dice = np.random.randint(1,7)
        if dice <= 2:
            step = max(0, step - 1)
        elif dice <= 5:
            step = step + 1
        else:
            step = step + np.random.randint(1,7)

        # Implement clumsiness
        if np.random.rand()<=0.001 :
            step = 0

        random_walk.append(step)
    all_walks.append(random_walk)

# Create and plot np_aw_t
np_aw_t = np.transpose(np.array(all_walks))
plt.plot(np_aw_t)
plt.show()

Plot the distribution

# Simulate random walk 500 times
all_walks = []
for i in range(500) :
    random_walk = [0]
    for x in range(100) :
        step = random_walk[-1]
        dice = np.random.randint(1,7)
        if dice <= 2:
            step = max(0, step - 1)
        elif dice <= 5:
            step = step + 1
        else:
            step = step + np.random.randint(1,7)
        if np.random.rand() <= 0.001 :
            step = 0
        random_walk.append(step)
    all_walks.append(random_walk)

# Create and plot np_aw_t
np_aw_t = np.transpose(np.array(all_walks))

# Select last row from np_aw_t: ends
ends = np_aw_t[-1,:]

# Plot histogram of ends, display plot
plt.hist(ends)
plt.show()

Calculate the odds

Chance =len(ends[ends>=60])/(len(ends))
Chance 

0.77