def sim(n):
    # runs a single trial.
    # assume car is in door 1.
    # returns True if switching leads to car, False otherwise.

    if random.randint(1, n) == 1:
        return False

    # host picks a door, so there are n - 2 remaining doors.

    return random.randint(1, n - 2) == 1

N = 4
TRIALS = 100000

successes = 0

for i in xrange(TRIALS):
    if sim(N):
        successes += 1

print float(successes) / TRIALS