Such is a general sketch of the large subject included under the term of the calculation of probabilities, which comprises not only the chances of games of hazard, insurances, lotteries, &c., but also the determination of future events from observations made relative to events of the same nature. This subject of inquiry dates only from the 17th century, and occupied the minds of Pascal, Huygens, Fermot, Bernouilli, Laplace, Fourier, Lacroix, Poisson, De Moivre; and in more modern times, Cournot, Quetelet, and Professor De Morgan.
In the matter of betting, or in estimating the 'odds' in betting, of course an acquaintance with the method must be of some service, and there can be no doubt that professional gamesters endeavoured to master the subject.
M. Robert-Houdin, in his amusing work, Les Tricheries des Grecs devoilees, has propounded some gaming axioms which are at least curious and interesting; they are presented as those of a professional gambler and cheat.
1. 'Every game of chance presents two kinds of chances which are very distinct,—namely, those relating to the person interested, that is, the player; and those inherent in the combinations of the game.'
In the former there is what must be called, for the want of a better name, 'good luck' or 'bad luck,' that is, some mysterious cause which at times gives the play a 'run' of good or bad luck; in the latter there is the entire doctrine of 'probabilities' aforesaid, which, according to M. Houdin's gaming hero, may be completely discarded for the following axiom:—
2. 'If chance can bring into the game all possible combinations, there are, nevertheless, certain limits at which it seems to stop. Such, for instance, as a certain number turning up ten times in succession at Roulette. This is possible, but it has never happened.'
Nevertheless a most remarkable fact is on record. In 1813, a Mr Ogden betted 1000 guineas to ONE guinea, that calling seven as the main, the caster would not throw that number ten times successively. Wonderful to relate! the caster threw seven nine times following. Thereupon Mr Ogden offered him 470 guineas to be off the bet—which he refused. The caster took the box again and threw nine,—and so Mr Ogden won his guinea!(56) In this case there seems to have been no suspicion whatever of unfair dice being used.
(56) Seymour Harcourt, The Gaming Calendar.
3. 'In a game of chance, the oftener the same combination has occurred in succession, the nearer we are to the certainty that it will not recur at the next cast or turn up. This is the most elementary of the theories on probabilities; it is termed the MATURITY OF THE CHANCES.'
'Hence,' according to this great authority, 'a player must come to the table not only "in luck," but he must not risk his money excepting at the instant prescribed by the rules of the maturity of the chances.'