Python -- program after refactoring returns different result

I'm computing 2 * Volume of sphere(dimension=4) / Volume of cylinder(dimension=4). What I'm getting wrong is the first approach to the problem. The second approach gives the right answer. Namely, I'm getting 1.14 when the answer should be 1.17. How do these programs differ? I can't spot the difference.

import random

# FIRST WAY

print('elegant solution')

coordinates = [0] * 3
alpha = 0
delta = 0.1
deltas = [0] * 3
n_trials = 1000000
n_hits = 0

for a in range(6):
    for i in range(n_trials):
        # gets random deltas, and random alpha for 4th dimension
        deltas = [random.uniform(-delta, delta) for coordinate in deltas]
        alpha = random.uniform(-1.0, 1.0)

        # sum of the (n - 1) first components
        sum_components = sum((coordinates[j] + deltas[j])**2 for j in range(3))

        # if the sample is inside the cylinder
        if sum_components < 1.0:
            coordinates = [coordinates[j] + deltas[j] for j in range(3)]

        # if the sample is inside the sphere
        if sum_components + alpha**2 < 1.0:
            n_hits += 1

    print (2.0 * float(n_hits) / float(n_trials)) # 2V_sph(4) / V_cyl(4) where V_sph=hits Vcyl=trials
    coordinates = [0] * 3
    n_hits = 0

# SECOND WAY

print('typical solution')

x, y, z, alpha = 0.0, 0.0, 0.0, 0.0
delta = 0.1
n_trials = 1000000
n_hits = 0

for a in range (6):
    for i in range(n_trials):
        # gets random deltas, and random alpha for 4th dimension
        del_x, del_y, del_z, alpha = random.uniform(-delta, delta), random.uniform(-delta, delta), random.uniform(-delta, delta), random.uniform(-1, 1)

        # if the sample is inside the cylinder
        if (x + del_x)**2 + (y + del_y)**2 + (z + del_z)**2 < 1.0:
            x, y, z = x + del_x, y + del_y, z + del_z

        # if the sample is inside the sphere
        if x**2 + y**2 + z**2 + alpha**2 < 1.0:
            n_hits += 1

    print (2.0 * n_hits / float(n_trials)) # 2V_sph(4) / V_cyl(4) where V_sph=hits Vcyl=trials
    x, y, z = 0.0, 0.0, 0.0
    n_hits = 0