Pious people have always been prone to declare that there is no such thing as chance. They have been afraid that belief in chance implied a disbelief in the omnipotence of God. Never were pious people more mistaken--or perhaps I should say misinformed. The doctrine of probabilities is one of those things belonging to mathematics which the pundits have decided it were better for us common people not to understand. So they have carefully refrained from stating it in interesting, or even human, language, pretending that we were barred from comprehension by the inadequacy of our intelligence and education. Nevertheless we all inhabit a world upon the phenomena of which the doctrine of probabilities is founded. We are compelled to live every day surrounded by events “obeying” the Law of the Greatest Probability. And those of us who have made any success in life have become pretty good mathematicians, though we may know no mathematical symbols beyond the signs of addition, subtraction and division. It is of course misleading to say that events _obey_ the law of the greatest probability. Events do not obey any of the laws which science has formulated. On the contrary, the laws were, in so far as they are laws and not mere errors, formulated in obedience to the events. But to say that there is no such thing as chance is to say that there is no such thing as ignorance, which to my mind is hardly a pious idea. For chance, rightly understood, is but the measure of our ignorance. Nothing more. Given total ignorance, the chance of guessing right is too remote to be calculable and can be expressed only by the meaningless formula, “nothing to infinity.” Given total knowledge, certainty leaves no room for probability. In all other circumstances, chance is the balance in which we weigh what we know against what we do not know. Gambling is called a vice because nobody ever uses the word except to describe some form of chance-taking which he considers vicious--the vice usually consisting in a foolish attempt to get something for nothing. It is considered particularly immoral to lose. But in a broad sense, everyone gambles who lives. I hope I will be pardoned, then, if I take my illustrations from actual games. If we know that a penny is a disk of equally weighted sides and is to be tossed in the air by an unknown amount of force which will cause it to turn over an unknown number of times, the chance of its falling head up is the same as that of its falling head down. We say the odds are even. If we do not know what a penny is, we cannot reckon the odds. If we know exactly what a penny is, know its present position in relation to the table-top, and know that it is going to turn over three times, say, there are no odds to calculate. Ignorance has been supplanted by knowledge.