from random import uniform as r
import matplotlib.pyplot as plt
import numpy as np

plt.figure(1)

for numrolls in range(1, 10):
    plt.subplot(1, 9, numrolls)
    mind = 50
    maxd = 250
    samplesize = 1000000

    rolls = []

    for i in range(samplesize):
        roll = []
        for ii in range(numrolls):
            roll.append(r(mind, maxd))
        rolls.append(np.average(roll))

    normal = np.random.normal(loc=(mind+maxd)/2, scale=(maxd-mind)/7, size=samplesize)

    plt.hist(normal, bins=(maxd-mind)/3, alpha=0.5, label="normal")
    plt.hist(rolls, bins=(maxd-mind)/3, alpha=0.5, label="simulation")
    plt.title("{0} - {1} @ {2} rolls".format(mind, maxd, numrolls))
    plt.xlabel("Value")
    plt.ylabel("Frequency")
    plt.legend(loc="upper right")
plt.show()