The St. Petersburg Paradox

#!/usr/bin/env
# -*- coding: utf-8 -*-
# Description: The game is played by flipping a fair coin until it comes up tails,
# and the total number of flips, n, determines the prize, which equals $2**n.
# Thus if the coin comes up tails the first time, the prize is $2**1 = $2, and the game ends.
# If the coin comes up heads the first time, it is flipped again.
# If it comes up tails the second time, the prize is $2**2 = $4, and the game ends.
# If it comes up heads the second time, it is flipped again. And so on.

import random, pylab

def simulation():
    power = 0
    while random.random() >= 0.5:
        power += 1
    return 2**power, power+1

def monte_carlo(entrence_price = 10, n_sim = 10000):
    equity = [0]
    flips = 0
    for i in xrange(n_sim):
        equity.append(equity[-1] - entrence_price + simulation()[0])
        flips += simulation()[1]
    equity.pop(0)
    return equity, flips

if __name__ == "__main__":
    pylab.figure(1)
    pylab.plot(range(1, 10001), monte_carlo()[0])
    pylab.show()