ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0
24 THE HANDBOOK OF PORTFOLIO MATHEMATICS
where: Wi=Dollars bet on theith horse to win.
W=Total dollarsin the win pool—i.e., total dollars bet on
all horses to win.
Si=Dollars bet on theith horse to show (or place).
S=Total dollarsin the show (or place) pool—i.e., total dol-
lars on all horses to show (or place).
i=The horse of your choice.If you’ve truly learned whatisinthis book you will use the Kelly for-
mula (more on thisin Chapter 4) to maximize the rate of your money’s
growth.How much to bet, however, becomes aniterative problem,in
that the more you bet on a particular horse to show, the more you will
change the mathematical expectation and payout—but not the probabili-
ties, since they are dictated by (Wi/W).Therefore, when you bet on the
horse to place, you alter the mathematical expectation of the bet and you
also alter the payout on that horse to place.Since the Kelly formulaisaf-
fected by the payout, you must be able toiterate to the correct amount to
bet.
Asin all winninggamblingor tradingsystems, employingthe winning
formulajust shownis far more difficult than you would think.Go to the
racetrack and try to apply this method, with the pools changingevery
60 seconds or so while you try to figure your formula and standinline
to make your bet and doitwithin seconds of the start of the race.The real-
time employment of any winningsystemis always more difficult than you
would think after seeingit on paper.Winning and Losing Streaks in the Random Process
We have already seen thatin flat-bettingsituationsinvolvinganindepen-
dent trials process you will lose at the rate of the house advantage.Toget
around this rule, manygamblers then try various bettingschemes that will
allow them to win more duringhot streaks than duringlosingstreaks, or
will allow them to bet more when they thinkalosingstreakislikely to end
and bet less when they think a winningstreakis about to end.Yet another
important axiom comesinto play here, whichis thatstreaks are no more
predictable than the outcome of the next event(thisis true whether we
are discussingdependent orindependent events).In the longrun, we can
predict approximately how many streaks of agiven length can be expected
from agiven number of chances.
Imagine that we flipacoin andit lands tails.We now have a streak of
one.If we flip the coin a second time, thereis a 50% chanceitwill come up