dice_paradox.py

# https://gilkalai.wordpress.com/2017/09/07/tyi-30-expected-number-of-dice-throws/
from pprint import pprint
import random

def toss():
    "Throw a die. Return the result if the result is even; otherwise None"
    n = random.randint(1,6)
    if n % 2: # odd
        return None
    return n

def toss_until_6():
    throws = []
    n = -1
    while n != 6:
        n = toss()
        if n:
            throws.append(n)
        else: # invalid run (gave an odd number)
            return None
    return throws

def get_n_valid_runs(n: int):
    runs = []
    while len(runs) < n:
        run = toss_until_6()
        if run:
            runs.append(run)
    return runs

def get_ave_length(n_good_runs: int, num_sides=6):
    """Ave length approaches the correct limit as n_good_runs increases.
    1000000 is enough to be accurate, and runs in a few seconds."""
    runs = get_n_valid_runs(n_good_runs)
    run_lengths = [len(run) for run in runs]
    return sum(run_lengths) / len(runs)