“It seems to me that every throw of sixes with a pair of dice is a manifest instance of chance.” Yes, of chance; but not of that chance the existence of which Mr. Peirce maintains—not of absolute chance. Every throw of dice, every toss of head or tail, are exactly determined by circumstances. We call it chance only in so far as we cannot calculate and predetermine the result. Suppose you take two large silver coins between your thumb and the first two fingers, one coin parallel to and a little above the other. Suppose tails are up in both. Drop the lower coin without an effort just as it would fall, about twenty inches, and you may be sure that, in spite of yourself, it will turn up head. Then drop the upper one and it will not turn, but plump right down showing tail. There are certain mechanical reasons for the one case as well as for the other. As soon as we know the law and can apply it, the case ceases to be an instance of chance. Dice, the roulette, and other games of chance are so arranged, that the determinating circumstances are too numerous and also too complex, one interfering with and being disturbed by the others, to admit of any adequate calculation or predetermination. An arrangement of conditions which in this way eludes the calculation of a definite set of possibilities, is called by Professor Kries _gleiche Spielräume_ or equal chances. And the province of equal chances is and will remain the proper sphere of the calculus of probabilities. Professor Nitsche objects to Kries’s proposition, saying that absolutely equal chances are impossible and an equal chance (_ein gleicher Spielräume_) is nothing but the objectification of a judgment of equal value.[13] We find no fault with Nitsche’s objection; there are no absolutely equal chances; and what is called “equal chance” means that the strength of two or several anticipations is of the same degree; that our belief and doubt as to the turning up of one, two, three, four, five, or six spots of a die are equally justified. The objective conditions which justify such equality of several expectations is what Kries (if we understand him correctly) calls _gleiche Spielräume_. But _gleiche Spielräume_ do not imply absolute chance. We might as well expect that all the six faces of a die should turn up simultaneously in one throw, as that any one of them should turn up by absolute chance.