Just a simulator for the problem posed by Geordie Rose here: http://dwave.wordpress.com/2008/03/03/i-am-gamblor/

gamblor.py

from __future__ import division
import random
totalPaid=0
numRuns=0
maxRuns=100000
maxRuns=10000
amountCharged=1
def flipCoins():
    result=0
    num=-1
    while result < 0.5:
        result=random.random()
        num+=1
#    if num >=3:
#        return 3
    else:
        return num 

dist={}
for i in xrange(maxRuns):
    numToGetTail = flipCoins()
#    print "numtails=", numToGetTail
    if dist.has_key(numToGetTail) == 0: dist[numToGetTail] = 1 
    else: dist[numToGetTail] += 1
    if numToGetTail > 0:
        payout = 2**(numToGetTail-1)
    else:
        payout = 0 
#    print "payout=", payout
    print
    totalPaid += payout - amountCharged
    numRuns += 1

print "average paid out=", totalPaid/numRuns
print "average paid out div by 4=", totalPaid/numRuns/4
print "total paid out=", totalPaid
for i in sorted(dist.keys()):
    print i,"=",dist[i]/maxRuns