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 ‘“math- 
ematical 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 mathe- 
matical 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, there- 
fore, 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. Fortu- 
nately, persons who deliberately gamble are in most com- 
munities 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