ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0
The Random Process and Gambling Theory 21profit of$ 699 .For numbers, the mathematical expectationis:ME=(699∗(1/1000))+((−1)∗(1−(1/1000)))
=(699∗.001)+((−1)∗(1−.001))
=(699∗.001)+((−1)∗.999)
=. 699 +(−.999)
=−. 3In other words your mathematical expectationis to lose 30 cents for
every dollar of action.Thisis far worse than any casinogame,including
keno.Bad as the probabilities areinagame like roulette, the mathematical
expectationin numbersis almost sixtimes worse.The onlygamblingsit-
uations that are worse than thisin terms of mathematical expectation are
most football pools and many of the state lotteries.Pari-Mutuel Betting
Thegames that offer seemingly the worst mathematical expectation be-
longto a family of what are called pari-mutuelgames.Pari-mutuel means
literally“to bet amongourselves.”Pari-mutuel bettingwas originatedin
the 1700s by a French perfume manufacturer named Oller.Monsieur Oller,
doublingas a bookie, used his perfume bottles as ticket stubs for his pa-
trons while he booked their bets.Oller would take the bets, from thisto-
tal pool he would take his cut, then he would distribute the remainder to
the winners.Today we have different types ofgames built on this same
pari-mutuel scheme, from state lotteries to football pools, from numbers
to horse racing.As you have seen, the mathematical expectations on most
pari-mutuelgames are atrocious.Yet these verygames also offer many sit-
uations that have a positive mathematical expectancy.
Let’s take numbers again, for example.We can approximate how much
moneyis betin total by takingthe averagewinningpurse size and dividing
itby1minus the take.In numbers, as we have said, the takeis 30%, so we
have 1−.3, or. 7 .Dividing1by.7yields 1. 42857 .If the average payoutis,
say,$1,400, then we can approximate the total purse as 1,400 times 1.42857,
or roughly$2,000.So step onein findingpositive mathematical expecta-
tionsin pari-mutuel situationsis to know or at least closely approximate
the total amountin the pool.
The next stepis to take this total amount and divideit by the to-
tal number of possible combinations.Thisgives the average amount bet
per combination.In numbers there are 1,000 possible combinations, soin