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import itertools
PYRAMID = [range(1, 5)] * 9
CUBIC = [range(1, 7)] * 6
pyramid_combs = itertools.product(*PYRAMID)
cubic_combs = itertools.product(*CUBIC)
d_pyr = dict((i, 0) for i in range(9, 37))
d_cub = dict((i, 0) for i in range(6, 37))
for p in pyramid_combs:
d_pyr[sum(p)] += 1
for p in cubic_combs:
d_cub[sum(p)] += 1
tot_cube = 4**9
tot_pyr = 6**6
prob_cube_winning = 0
for k, v in d_pyr.iteritems():
event_prob = float(sum([y for x, y in d_cub.iteritems() if x < k])) / tot_pyr
tot_prob = (event_prob * v) / tot_cube
prob_cube_winning += tot_prob
print prob_cube_winning
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