538_play_250_to_play.py

"""
http://fivethirtyeight.com/features/should-you-pay-250-to-play-this-casino-game/

Suppose a casino invents a new game that you must pay $250 to play. The game
 works like this:

The casino draws random numbers between 0 and 1, from a uniform distribution. It
 adds them together until their sum is greater than 1, at which time it stops
drawing new numbers. You get a payout of $100 each time a new number is drawn.
"""

import random
import collections

ITER = 100000
COST = 250
gain = collections.Counter()

for x in range(ITER):
    remain = 1
    g = 0
    while(remain > 0):
        remain -= random.random()
        g += 100
    gain[g - COST] += 1


# Utility
utility = sum(k*v for (k, v) in gain.items())/ITER
print(utility)