Rogues den probabilities

import random

prob = 0.249
sample = 10000
samples = []
for _ in range(sample):
    pieces = 0
    tries = 0
    while pieces < 5:
        tries += 1
        if random.random() < prob:
            pieces += 1
    samples.append(tries)

print(list(sorted(samples))[len(samples)//2])