Free Throws That Reinforce Themselves

Tom makes his first free throw and misses his second. From the third attempt on, the probability that he makes attempt $n$ equals the fraction of his first $n-1$ attempts that were makes.

import random

def practice(attempts=100):
    made, taken = 1, 2                      # attempt 1 made, attempt 2 missed
    for _ in range(attempts - 2):
        if random.random() < made / taken:
            made += 1
        taken += 1
    return made

print(sum(practice() for _ in range(10**6)) / 10**6)

What number does this print, up to simulation noise?

Answer format: enter an integer.