Every event is a result of causes:  but the multitude of forces and the variety of collocations being immeasurably great, the overwhelming majority of events occurring about the same time are only related by Causation so remotely that the connection cannot be followed.  Whilst my pen moves along the paper, a cab rattles down the street, bells in the neighbouring steeple chime the quarter, a girl in the next house is practising her scales, and throughout the world innumerable events are happening which may never happen together again; so that should one of them recur, we have no reason to expect any of the others.  This is Chance, or chance coincidence.  The word Coincidence is vulgarly used only for the inexplicable concurrence of interesting events—­“quite a coincidence!”

On the other hand, many things are now happening together or coinciding, that will do so, for assignable reasons, again and again; thousands of men are leaving the City, who leave at the same hour five days a week.  But this is not chance; it is causal coincidence due to the custom of business in this country, as determined by our latitude and longitude and other circumstances.  No doubt the above chance coincidences—­writing, cab-rattling, chimes, scales, etc.—­are causally connected at some point of past time.  They were predetermined by the condition of the world ten minutes ago; and that was due to earlier conditions, one behind the other, even to the formation of the planet.  But whatever connection there may have been, we have no such knowledge of it as to be able to deduce the coincidence, or calculate its recurrence.  Hence Chance is defined by Mill to be:  Coincidence giving no ground to infer uniformity.

Still, some chance coincidences do recur according to laws of their own:  I say some, but it may be all.  If the world is finite, the possible combinations of its elements are exhaustible; and, in time, whatever conditions of the world have concurred will concur again, and in the same relation to former conditions.  This writing, that cab, those chimes, those scales will coincide again; the Argonautic expedition, and the Trojan war, and all our other troubles will be renewed.  But let us consider some more manageable instance, such as the throwing of dice.  Every one who has played much with dice knows that double sixes are sometimes thrown, and sometimes double aces.  Such coincidences do not happen once and only once; they occur again and again, and a great number of trials will show that, though their recurrence has not the regularity of cause and effect, it yet has a law of its own, namely—­a tendency to average regularity.  In 10,000 throws there will be some number of double sixes; and the greater the number of throws the more closely will the average recurrence of double sixes, or double aces, approximate to one in thirty-six.  Such a law of average recurrence is the basis of Probability.  Chance being the fact of coincidence without assignable cause, Probability is expectation based on the average frequency of its happening.