[numpy] Dice rolling simulator

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
from sklearn.neighbors import KernelDensity

ax = plt.figure().gca()
ax.xaxis.set_major_locator(MaxNLocator(integer=True))

class Die():
    num_sides=6
    def roll(self):
        return np.random.randint(1,self.num_sides+1)

# create two D6 dice
die_1 = Die()
die_2 = Die()
die_3 = Die()
die_4 = Die()

# make some rolls, and store results in a list.
results = []
for roll_num in range(5000):
 result = die_1.roll() + die_2.roll()# + die_3.roll() + die_4.roll()
 results.append(result)

# analyze the results.
model = KernelDensity(bandwidth=2, kernel='gaussian')
sample = np.array(results).reshape((len(results), 1))
model.fit(sample)

values = np.asarray([value for value in range(1, 14)])
values = values.reshape((len(values), 1))
probabilities = model.score_samples(values)
probabilities = np.exp(probabilities)

max_result = die_1.num_sides + die_2.num_sides# + die_3.num_sides + die_4.num_sides

x_max = die_1.num_sides + die_2.num_sides# + die_3.num_sides + die_4.num_sides

plt.hist(results, bins=np.arange(1, max_result+2)-.5, histtype = 'bar',
         rwidth=0.8, facecolor = 'gray', edgecolor="k", density=True)

plt.plot(values[:], probabilities)
plt.title("Dice Plot")
plt.xlabel("Results")
plt.ylabel("Density")

plt.show()

plt.hist(results, bins=np.arange(1, max_result+2)-.5, histtype = 'bar',
         rwidth=0.8, facecolor = 'gray', edgecolor="k")

plt.title("Dice Plot")
plt.xlabel("Results")
plt.ylabel("Frequency")

plt.show()