ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0
16 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 1.4 Results of 60 coin tosses with a 5% house advantagethis scenario, ruinisinevitable—as the upper standard deviations beginto
bend down (to eventually cross below zero).
Let’s examine what happens when we continue to play agame with a
negative mathematical expectation.N Std Dev Expectation +or−1SD10 1.58 −.5 +1.08 to−2.08
100 5.00 −50to− 10
1,000 15.81 − 50 −34.19 to−65.81
10,000 50.00 − 500 −450 to− 550
100,000 158.11 −5,000 −4,842 to−5,158
1,000,000 500.00 −50,000 −49,500 to−50,500The principle of ergodicityis at work here.It doesn’t matterif one
persongoes to a casino and bets$1 one million timesin succession or
if one million people come and bet$1 each all at once.The numbers are
the same.At one million bets,it would take more than 100 standard devia-
tions away from the expectation before the casino started to lose money!
Hereis the Law of Averages at work.By the same account,if you were
to make one million$1 bets at a 5% house advantage,it would be equally
unlikely for you to make money.Many casinogames have more than a
5% house advantage, as does most sports betting.Tradingthe markets