Prisoner Box Problem

prisoners.py

import random

PRISONERS = 100

def search(i, boxes):
    next_box = i
    for _ in range(PRISONERS // 2):
        if i == boxes[next_box]:
            return True
        next_box = boxes[next_box]
    return False

def run():
    boxes = list(range(PRISONERS))
    random.shuffle(boxes)

    for i in range(PRISONERS):
        if not search(i, boxes):
            return False
    return True

def sim(runs):
    return sum(1 if run() else 0 for _ in range(runs)) / runs