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 statistics
 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 estimate.
 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 defining
 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 conditions,
 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