Since therefore an entire indifference is essential to chance, no one
chance can possibly be superior to another, otherwise than as it is
composed of a superior number of equal chances. For if we affirm that
one chance can, after any other manner, be superior to another, we must
at the same time affirm, that there is something, which gives it the
superiority, and determines the event rather to that side than the
other: That is, in other words, we must allow of a cause, and destroy
the supposition of chance; which we had before established. A
perfect and total indifference is essential to chance, and one total
indifference can never in itself be either superior or inferior to
another. This truth is not peculiar to my system, but is acknowledged by
every one, that forms calculations concerning chances.
And here it is remarkable, that though chance and causation be directly
contrary, yet it is impossible for us to conceive this combination of
chances, which is requisite to render one hazard superior to another,
without supposing a mixture of causes among the chances, and a
conjunction of necessity in some particulars, with a total indifference
in others. Where nothing limits the chances, every notion, that the most
extravagant fancy can form, is upon a footing of equality; nor can there
be any circumstance to give one the advantage above another. Thus unless
we allow, that there are some causes to make the dice fall, and preserve
their form in their fall, and lie upon some one of their sides, we can
form no calculation concerning the laws of hazard. But supposing these
causes to operate, and supposing likewise all the rest to be indifferent
and to be determined by chance, it is easy to arrive at a notion of a
superior combination of chances. A dye that has four sides marked with
a certain number of spots, and only two with another, affords us an
obvious and easy instance of this superiority. The mind is here limited
by the causes to such a precise number and quality of the events; and at
the same time is undetermined in its choice of any particular event.