Estimate waiting times for the Plounge AMA

Plounge_AMA_Waiting_Simulator.py

from random import randint, choice

waitlist_growths = [2, 2, 3, 4, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 8, 9, 9, 9, 10, 13, 14, 17]
  # I took the most recent 166 top-level comments to the AMA
  # signup thread, grouped them by week, and counted the size of
  # each group.

# http://www.reddit.com/r/MyLittleShellbullet17/comments/1pnhpx/ama_sign_up/cgko9z8?context=5

def howlong(
        initial_waitlist_len = 483,
        amas_per_week = 4):
    waitlist_len = initial_waitlist_len
    weeks_elapsed = 0
    while 1:
        for ama in range(amas_per_week):
            while 1:
                if waitlist_len == 0:
                  # You're the only person left, so you must be
                  # picked.
                    return weeks_elapsed
                if randint(1, waitlist_len + 1) == 1:
                  # You were picked.
                    return weeks_elapsed
                if randint(0, 1):
                  # Shelly passed over this name.
                    # If it came up again, he'd probably pass over it again.
                    # So, let's remove it from the list.
                    waitlist_len -= 1
                break
            # This person gets an AMA, so they're removed from
            # the waitlist.
            waitlist_len -= 1
        # The waitlist grows.
        waitlist_len += choice(waitlist_growths)
        # A week passes.
        weeks_elapsed += 1

mean = lambda v: float(sum(v)) / len(v)

N = 10000
days = sorted([7 * howlong() for _ in xrange(N)])
print '[{} - {} - {}]'.format(
    days[int(N*.025)], days[int(N/2)], days[int(N*.975)])
print 'Mean:', int(round(mean(days)))
print 'Proportion >=:'
for y in (1, 2, 3):
    print '   ', y, 'year' + ('' if y == 1 else 's') + ':',  mean([int(x >= y*365) for x in days])