from __future__ import division
import numpy as np

num_sides = 6
bound = 200
index = 66
num_simulations = int(1e7)

rolls = np.random.randint(1, high=num_sides+1, size=[index, num_simulations])
accum = np.sum(rolls, axis=0)
samples = accum <= bound
mean = np.mean(samples)
var = np.var(samples)

print('mean: {}, var: {}'.format(mean, var))