How many birthdays/day as a function of your friend list size?

bdaydist.py

#!/usr/bin/env python

import sys
import random

friends = int(sys.argv[1])
counts = {}
iterations = 1000


def bday_per_day():
    days = {}
    for friend in range(0, friends):
        day = random.randint(1, 365)
        days[day] = days.get(day, 0) + 1

    for day in range(1, 366):
        birthdays = days.get(day, 0)
        counts[birthdays] = counts.get(birthdays, 0) + 1

for run in range(0, iterations):
    bday_per_day()

for count in sorted(counts, key=counts.get, reverse=True):
    print "%d birthdays: %0.03f times/year" % (
        count, counts[count] / float(iterations))

$ ./bdaydist.py 401
1 birthdays: 133.954 times/year
0 birthdays: 121.482 times/year
2 birthdays: 73.353 times/year
3 birthdays: 26.869 times/year
4 birthdays: 7.380 times/year
5 birthdays: 1.617 times/year
6 birthdays: 0.291 times/year
7 birthdays: 0.043 times/year
8 birthdays: 0.008 times/year
9 birthdays: 0.001 times/year