ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0
The Random Process and Gambling Theory 17is a zero-sumgame.However, thereis a small draininvolvedin the way
of commissions, fees, and slippage.Often these costs can runin excess
of 5%.
Next, let’s examine the statistics of a 100-coin-tossgame with and with-
out a 5% house advantage:Std. Deviations from
Center Fair 50/50 Game5% House Advantage
Game+ 3 + 15 + 10
+ 2 + 10 + 5
+ 1 + 50
00 − 5
− 1 − 5 − 10
− 2 − 10 − 15
− 3 − 15 − 20As can be seen, at 3 standard deviations, which we can expect to be
the outcome 99.73% of the time, we will win or lose between+15 and− 15
unitsinafairgame.At a house advantage of 5%, we can expect our final
outcome to be between+10 and−20 units at the end of 100 trials.At 2
standard deviations, which we can expect to occur 95% of the time, we win
or lose within+or− 10 inafairgame.At a 5% house advantagethisis
+5 and−15 units.At 1 standard deviation, where we can expect the final
outcome to be with 68% probability, we win or lose up to 5 unitsinafair
game.Yetinthegame where the house has the 5% advantage we can ex-
pect the final outcome to be between winningnothingand losing10 units!
Note that at a 5% house advantageitis notimpossible to win money after
100 trials, but you would have to do better than 1 whole standard devia-
tion to do so.In the Normal Distribution, the probability of doingbetter
than 1 whole standard deviation, you will be surprised to learn,is only. 1587!
Noticein the previous example that at 0 standard deviations from the
center line (thatis, at the center lineitself), the amount lostis equal to
the house advantage.For the fair 50/50game, thisis equal to 0.You would
expect neither to win nor to lose anything.In thegame where the house
has the 5% edge, you would expect to lose 5%, 5 units for every 100 trials,
at 0 standard deviations from the center line.So you can say thatin flat-
betting situations involving an independent process, you will lose at the
rate of the house advantage.