ciding what chance will and will not account for, although our
exposition amounts only to making more clear what it is that we mean
by chance as distinguished from assignable reason. I would suggest
that in deciding what chance will not account for, we make regressive
application of a principle which may be called the principle of Equal
and Unequal Alternatives, and which may be worded as follows:--

Of a given number of possible alternatives, all equally
possible, one of which is bound to occur at a given time, we
expect each to have its turn an equal number of times in the
long run. If several of the alternatives are of the same
kind, we expect an alternative of that kind to recur with a
frequency proportioned to their greater number. If any of the
alternatives has an advantage, it will recur with a frequency
proportioned to the strength of that advantage.

Situations in which alternatives are absolutely equal are rare in
nature, but they are artificially created for games "of chance," as in
tossing a coin, throwing dice, drawing lots, shuffling and dealing a
pack of cards. The essence of all games of chance is to construct a
number of equal alternatives, making them as nearly equal as possible,
and to make no prearrangement which of the number shall come off. We
then say that this is determined by chance. If we ask why we believe
that when we go on bringing off one alternative at a time, each will
have its turn, part of the answer undoubtedly is that given by De
Morgan, namely, that we know no reason why one should be chosen rather
than another. This, however, is probably not the whole reason for our
belief. The rational belief in the matter is that it is only in the
long run or on the average that each of the equal alternatives will
have its turn, and this is probably founded on the experience of
actual trial. The mere equality of the alternatives, supposing them
to be perfectly equal, would justify us as much in expecting that
each would have its turn in a single revolution of the series, in one
complete cycle of the alternatives. This, indeed, may be described
as the natural and primitive expectation which is corrected by
experience. Put six balls in a wicker bottle, shake them up, and roll
one out: return this one, and repeat the operation: at the end of six
draws we might expect each ball to have had its turn of being drawn
if we went merely on the abstract equality of the altern