random_talk.py

from random import random

max_population = 10
iterations = 100000

for n in range(2, max_population):
    probability = 1.0/n
    success_count, fail_count = 0, 0
    success_rounds, fail_rounds = [], []
    for j in range(iterations):
        round = 0
        not_talked = n
        while True:
            round += 1
            talked = 0
            for i in range(not_talked):
                if random() < probability:
                    talked += 1
            if talked == 1:
                # success case
                not_talked -= 1
            elif talked > 1:
                # fail case
                fail_count += 1
                fail_rounds.append(round)
                break
            if not_talked == 0:
                # everyone has talked 
                success_count += 1
                success_rounds.append(round)
                break
    print (
        n,  # population
        100.0 * success_count / iterations,  # success percetage
        100.0 * fail_count / iterations,  # fail percetage
        sum(success_rounds) * 1.0 / len(success_rounds),  # average of rounds of successful games
        sum(fail_rounds) * 1.0 / len(fail_rounds),  # average of rounds of failed games
    )