A monte carlo simulation of a very particular kind of dice pool.

harperpool.py

#!/usr/bin/env python
# A simple monte carlo simulation for a specific kind of die pool.
#
# Usage: ./pool.py --trials=1000 4d6+3d8

import collections
import random

def main(args):
    result = collections.defaultdict(lambda: 0)
    for trial in range(args.trials):
        highest, count = 0, 0
        pool = sorted(roll(args.pattern[0]), reverse=True)
        highest = pool[0][0]
        for val, die in pool[1:]:
            if val == die:
                count += 1
        result[highest+count] += 1

    for val in result:
        print '%02d: %0.5f' % (val, result[val] / float(args.trials))


def roll(pattern):
    for dice in pattern.split('+'):
        n, d = int(dice[0]), int(dice[2])
        for _ in range(n):
            yield (random.randrange(1, d+1), d)


if __name__ == '__main__':
    import argparse
    parser = argparse.ArgumentParser()
    parser.add_argument('pattern', metavar='P', type=str, nargs=1)
    parser.add_argument('--trials', type=int, default=1000)
    main(parser.parse_args())