Sec. 2] THE RISK ELEMENT 269 
circumstances of each case; and his final estimate of the 
chance that a particular building will burn, a particular 
ship founder, or a particular person die, is based on all the 
data available, among which the data supplied by statis- 
tics are an important but by no means the sole element. 
To apply this idea of chance to an economic example, 
consider a gold mine. What is the chance that it conceals 
a rich lead of ore? The ordinary man makes an estimate, 
based on his experience or inexperience. The geologist 
has additional knowledge and would make a different esti- 
mate. In actual fact, however, gold is either actually 
there in certain definite quantities, or is totally absent. 
It is a coin held in nature’s closed hand. 
§2 
But, in showing that chance is purely a psychological 
and not an objective magnitude, we are still far from de- 
fining chance as a mathematical magnitude. In order to 
measure chance, it is necessary to state (1) when two 
chances are equal or unequal; and (2) when one chance 
bears any given ratio to the other. 
The chance of one event is said to be equal to the chance 
of another in the mind of a particular individual, when that 
individual has no inclination to believe that one will occur 
rather than the other. One of the chances is said to exceed 
the other when the individual is “inclined to believe” 
that one event will occur rather than the other. The test 
of the equality of two chances is mere indecision of opinion 
— opinion exactly and evenly balanced. 
Next comes the question of the ratio of two chances. 
When it is ‘said that the odds in favor of one event as 
compared with another are two to one, the meaning is 
that out of three equally probable combinations of condi- 
tions, two imply the first event and only one the second. 
Thus, if there are three cards in a hat, of which it is 
known that only one will draw a prize, the chance against