Temtem SV distribution script

from pprint import pprint
from collections import defaultdict

# Number of stats
STATS = 7

# Max SV value
MAX_SV = 50

# Minimum total SVs
MIN_TOTAL_SVS = 168

def calc_distribution():
    # distribution[(n, k)] = number of ways to get total svs n with exactly k perfect svs
    distribution = {(0, 0): 1}
    for stat in range(STATS):
        new_distribution = defaultdict(int)
        for sv_sum, num_perfect in distribution:
            for sv in range(1, MAX_SV+1):
                new_sum = sv_sum + sv
                new_perfect = num_perfect + (sv == MAX_SV)
                new_distribution[new_sum, new_perfect] += distribution[sv_sum, num_perfect]
        distribution = new_distribution
    return distribution

# Reduce on perfect_sv count given that sv_sum >= min_sv_sum
# Returns map of perfect_svs -> number of ways that this can be generated.
def reduce_distribution(d, min_sv_sum):
    distribution = defaultdict(int)
    for sv_sum, num_perfect in d:
        if sv_sum < min_sv_sum:
            continue
        distribution[num_perfect] += d[sv_sum, num_perfect]
    return distribution

def main():
    distribution = calc_distribution()
    x = reduce_distribution(distribution, MIN_TOTAL_SVS)
    pprint(dict(x))
    print "Total: %d" % sum(x.values())
    print "Probability of 1+ perfect SV: %f" % (float(sum(x.values()) - x[0]) / sum(x.values()))


if __name__ == '__main__':
    main()