Calculate expected value of D&D ability generation

abilities.py

#!/usr/bin/env python

import random
import sys


def d6():
    return random.randrange(1, 7)


def fourD6():
    return [d6() for _ in range(4)]


def topD6():
    return sorted(fourD6(), reverse=True)[:3]


def sumD6():
    return sum(topD6())


ITERATIONS = 1000000
histo = [None, None, None] + [0] * 16
min_, max_, total = 2 ** 32, -1 , 0

for _ in range(ITERATIONS):
    s = sumD6()
    print(f"{s}", file=sys.stderr)
    min_ = min(min_, s)
    max_ = max(max_, s)
    total += s
    histo[s] += 1

ev = total / ITERATIONS
print(f"min was {min_}", file=sys.stderr)
print(f"max was {max_}", file=sys.stderr)
print(f"EV is {ev}")

cum = 0.0
for roll, count in enumerate(histo[3:], 3):
    pc = count / ITERATIONS
    cum += (100.0 * pc)
    print(f"{roll:2d} : {pc * 100.0:6.2f}% {cum:6.2f}% ({count})")