On Games (-1899)

"I believe the calculation of the quantity of probability might be improved to a very useful and pleasant speculation, and applied to a great many events which are accidental, besides those of games; only these cases would be infinitely more confused, as depending on chances which the most part of men are ignorant of." (John Arbuthnot, "Of the Laws of Chance", 1692)

"But here it seems to me that we are at a loss, since one is at liberty to do this only just in very few cases, and indeed one may hardly succeed else where other than in games of chance, the first inventors of which, doing their best to bring about fairness, arranged things for themselves in such a way that the numbers of cases in which gain or loss ought to follow, might be definite and known, and that all these cases might happen with equal facility. For in most other situations depending either on the working of nature or on the judgement of men, this is by no means the case." (Jacob Bernoulli, "Ars Conjectandi" ["The Art of Conjecturing"], 1713)

"The man of system, on the contrary, is apt to be very wise in his own conceit; and is often so enamoured with the supposed beauty of his own ideal plan of government, that he cannot suffer the smallest deviation from any part of it. He goes on to establish it completely and in all its parts, without any regard either to the great interests, or to the strong prejudices which may oppose it. He seems to imagine that he can arrange the different members of a great society with as much ease as the hand arranges the different pieces upon a chess-board. He does not consider that the pieces upon the chess-board have no other principle of motion besides that which the hand impresses upon them; but that, in the great chess-board of human society, every single piece has a principle of motion of its own, altogether different from that which the legislature might choose to impress upon it. If those two principles coincide and act in the same direction, the game of human society will go on easily and harmoniously, and is very likely to be happy and successful. If they are opposite or different, the game will go on miserably, and the society must be at all times in the highest degree of disorder." (Adam Smith, "The Theory of Moral Sentiments", 1759)

"In another sense, the term ‘rule’ is used for ‘means’: to recognize an underlying truth through a single obviously relevant feature enables us to derive a general law of action from this feature. Rules in games are like this, and so are the short cuts used in mathematics, and so on." (Carl von Clausewitz, "On War", 1832)

"In short, absolute, so-called mathematical factors never find a firm basis in military calculations. From the very start there is an interplay of possibilities, probabilities, good luck and bad that weaves its way throughout the length and breadth of the tapestry. In the whole range the human activities war most closely resembles a game of cards." (Carl von Clausewitz, "On War", 1832)

"[...] in the game of heads or tails, the arrival of heads results from the constitution of the tossed coin. It can be regarded as physically impossible that the chances of both outcomes are the same; however, if that constitution is unknown to us, and we did not yet try out the coin, the probability of heads is for us absolutely the same as that of tails. Actually, we have no reason to believe in one of these events rather than in the other one. This will not be the same after many tosses of the coin: the chance of each side does not change during the trials, but for someone who knows their results, the probability of the future occurrence of heads and tails varies in accord with the number of times they happened." (Siméon-Denis Poisson, "Règles générales des probabilités", 1837)

"The law of large numbers is noted in events which are attributed to pure chance since we do not know their causes or because they are too complicated. Thus, games, in which the circumstances determining the occurrence of a certain card or certain number of points on a die infinitely vary, can not be subjected to any calculus. If the series of trials is continued for a long time, the different outcomes nevertheless appear in constant ratios. Then, if calculations according to the rules of a game are possible, the respective probabilities of eventual outcomes conform to the known Jakob Bernoulli theorem. However, in most problems of contingency a prior determination of chances of the various events is impossible and, on the contrary, they are calculated from the observed result." (Siméon-Denis Poisson, "Researches into the Probabilities of Judgements in Criminal and Civil Cases", 1837)

"The chemists who uphold dualism are far from being agreed among themselves; nevertheless, all of them in maintaining their opinion, rely upon the phenomena of chemical reactions. For a long time the uncertainty of this method has been pointed out: it has been shown repeatedly, that the atoms put into movement during a reaction take at that time a new arrangement, and that it is impossible to deduce the old arrangement from the new one. It is as if, in the middle of a game of chess, after the disarrangement of all the pieces, one of the players should wish, from the inspection of the new place occupied by each piece, to determine that which it originally occupied." (Auguste Laurent, "Chemical Method", 1855)

"The chess board is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of Nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance." (Thomas H Huxley, "A Liberal Education", 1868)

"And as the number of combinations that can be made on the chess-board, is so great that probably no two games exactly alike were ever played; so no two games which the student plays with nature to wrest from her hidden truths, which were worth playing at all, ever made use of quite the same methods in quite the same way." (Alfred Marshall, "Principles of Economics", 1890)

"Observe, finally, that this induction is possible only if the same operation can be repeated indefinitely. That is why the theory of chess can never become a science: the different moves of the game do not resemble one another." (Henri Poincaré, "On the Nature of Mathematical Reasoning", 1894)