ascending_dice.py

#!/usr/bin/env python3
#
# Answer to the 538 Riddler Express for Nov 12, 2021
# Author: Lowell Vaughn

def generate_roles(dice):
    """ Generates a list of lists enumerating all of outcomes of rolling a set of dice of
        various numbers of sides. For instance, generate_roles([4, 6, 8]) will return a list
        of all outcomes from rolling  4-sided, 6-sized, and 8-sided die (in that order)
    """
    if not dice:
        yield []
    else:
        for rest in generate_roles(dice[1:]):
            for i in range(dice[0]):
                yield [i + 1] + rest


def is_asc(roles):
    """ Returns true of a list's values are strictly increasing in size """
    return all(a[0] < a[1] for a in zip(roles[:-1], roles[1:]))


def get_probs(dice_sizes):
    """ Determines the probability that the outcome of rolling the dice is strictly
        increasing for the given set of dice sizes
    """
    n_seq = 0
    asc_seq = 0
    for sequence in generate_roles(dice_sizes):
        n_seq += 1
        if is_asc(sequence):
            asc_seq += 1

    return asc_seq, n_seq, asc_seq / n_seq


print("4, 6, 8", get_probs((4, 6, 8)))
print("4, 6, 8, 10, 12, 20", get_probs((4, 6, 8, 10, 12, 20)))