THE RISK ELEMENT

§5

The main application of risk to capital valuation is,
however, not to the rate of interest, but to the income
, items themselves. To this application we now address
ourselves. Let us begin by considering the case in which
the element of discounting is wholly absent. The simplest
case is that of ordinary gambling. If one invests in a
lottery ticket where there is one chance in ten of drawing
a prize of $50, it is evident that the price of the ticket
must be considerably less than $50, which is the income
. it may yield. Mathematicians have called the product
of the prize multiplied by its probability, the ‘“mathematical
 value’ of the chance. In the present instance
this “mathematical value” will be $50 x 5, or $5.
If a professional gambler should always pay the mathematical
 value of the chances, he would, in the long run,
probably come out about even, as is well known from
“Bernoulli’s Theorem.” Thus, if he continued to try for
such $50 prizes, paying each time $5, he would probably
win about one time in ten. In a thousand trials, therefore,
 he might expect to win 100 times, spending $5 each
for his 1000 tickets, or $5000, and receiving $50 each for
his 100 prizes, or $5000.
But the actual price which one will pay is not necessarily
the mathematical value of the chance. It may be higher ;
it is usually lower. The gambler is usually a person who
will pay more than the mathematical value of the chance.
At Monte Carlo, the “bank” makes its profit in this way,
although its victims know full well that they are paying
more than the mathematical value of their chances.. The
consequence, of course, is ruin to most of them. Fortunately,
 persons who deliberately gamble are in most communities
 in the minority. The ordinary man 1s unwilling
to pay even the full mathematical value of the chance.
He is reluctant to assume any risks, and is, on the