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18 THE HANDBOOK OF PORTFOLIO MATHEMATICS
Mathematical Expectation Less than Zero Spells Disaster
Thisbrings us to another axiom, which can be stated as follows:In a neg-
ative expectancy game, there is no money management scheme that will
make you a winner. If you continue to bet, regardless of how you man-
age your money, it is almost certain that you will be a loser, losing your
entire stake regardless of how large it was to start.
This sounds like somethingto think about.Negative mathematical ex-
pectations (regardless of how negative) have broken apart families and
caused suicides and murders and all sorts of other things the bettors
weren’t bargainingfor.I hope you can see what anincredibly losingpropo-
sitionitis to make bets where thereisanegative expectancy, for even a
small negative expectancy will eventually take every cent you have.All at-
tempts to outsmart this process are mathematically futile.Don’tget this
idea confused with whether or not thereis a dependent orindependent tri-
als processinvolved;it doesn’t matter.If the sum of your betsisanegative
expectancy, you arein a losingproposition.
As an example,if you arein a dependent trials process where you have
an edgein 1 bet out of 10, then you must bet enough on the bet for which
you have an edge so that the sum of all 10 betsis a positive expectancy
situation.If you expect to lose 10 cents on average for 9 of the 10 bets,
but you expect to make 10 cents on the 1 out of 10 bets where you know
you have the edge, then you must bet more than 9 times as much on the
bet where you know you have the edge,just to have a net expectation of
comingout even.If you bet less than that, you are stillinanegative ex-
pectancy situation, and complete ruinis all but certainif you continue to
play.
Many people have the mistakenimpression thatif they play a negative
expectancygame, they will lose a percentage of their capital relative to
the negative expectancy.For example, when most people realize that the
mathematical expectationin rouletteis5.26% they seem to think this means
thatif theygotoacasino and play roulette they can expect to lose, on
average, 5.26% of their stake.Thisis a dangerous misconception.The truth
is that they can expect to lose 5.26% of theirtotal action, not of their entire
stake.Suppose they take$500 to play roulette.If they make 500 bets of
$20 each, their total actionis$10,000, of which they can expect to lose
5 .26%, or$526, more than their entire stake.
The only smart thingto dois bet only when you have a positive
expectancy.Thisis not so easily a winningproposition as negative ex-
pectancy bettingisalosingproposition, as we shall seein a later chapter.
You must bet specific quantities, which will be discussed at length.For the
time being, though, resolve to bet only on positive expectancy situations.