How about this: People shoot in a random order (now everyone has the same chance of making it to the next round. Is it 1/e?) import numpy as np class Shoo

How about this: People shoot in a random order (now everyone has the same chance of making it to the next round. Is it 1/e?) import numpy as np class Shooter: def __init__(self): self.dead = False self.right = None # The person to the right def simulate(n): # Simulates a round with n shooters # Returns the ratio of survivors shooters = [Shooter() for i in range(n)] for i, shooter in enumerate(shooters): shooter.right = shooters[(i+1) % len(shooters)] np.random.shuffle(shooters) HIT_PROBABILITY = 1/6 survivors = n for shooter in shooters: if not shooter.dead: if np.random.random() < HIT_PROBABILITY: shooter.right.dead = True survivors = survivors - 1 return survivors/n Simulations suggest that the survival probabilities do not converge to 6/7 if you add shuffling. This makes sense, since the survival probability for the random shuffling version must be strictly less than if you are guaranteed to go first. >>>sum([simulate(10000) for j in range(1000)])/1000 0.8463075999999998