Probability or reasoning from conjecture may be divided into two kinds, viz. that which is founded on chance, and that which arises from causes.  We shall consider each of these in order.

The idea of cause and effect is derived from experience, which presenting us with certain objects constantly conjoined with each other, produces such a habit of surveying them in that relation, that we cannot without a sensible violence survey them iii any other.  On the other hand, as chance is nothing real in itself, and, properly speaking, is merely the negation of a cause, its influence on the mind is contrary to that of causation; and it is essential to it, to leave the imagination perfectly indifferent, either to consider the existence or non-existence of that object, which is regarded as contingent.  A cause traces the way to our thought, and in a manner forces us to survey such certain objects, in such certain relations.  Chance can only destroy this determination of the thought, and leave the mind in its native situation of indifference; in which, upon the absence of a cause, it is instantly re-instated.

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.