game-with-chocolates.py

import random

n_start_milk_choc = 2
n_start_black_choc = 8

n_trials = 1000000
n_milk_last = 0

for _ in range(n_trials):
    prev_pulled_choc = None

    n_milk_choc = n_start_milk_choc
    n_black_choc = n_start_black_choc
    
    while n_black_choc > 0 and n_milk_choc > 0:
        pulled_choc = random.random() < n_black_choc / (n_black_choc + n_milk_choc)

        if prev_pulled_choc is None or prev_pulled_choc == pulled_choc:
            if pulled_choc == 1:
                n_black_choc -= 1
            else:
                n_milk_choc -= 1

            if prev_pulled_choc is None:
                prev_pulled_choc = pulled_choc
                
        elif prev_pulled_choc != pulled_choc:
            prev_pulled_choc = None

    assert n_black_choc != 0 or n_milk_choc != 0
    n_milk_last += (n_milk_choc > 0)

print("Fraction of simulations with last milk chocolate", n_milk_last / n_trials)