CHAPTER VIII. THE DOCTRINE OF PROBABILITIES APPLIED TO GAMBLING.
A distinction must be made between games of skill and games of chance. The former require application, attention, and a certain degree of ability to insure success in them; while the latter are devoid of all that is rational, and are equally within the reach of the highest and lowest capacity. To be successful in throwing the dice is one of the most fickle achievements of fickle fortune; and therefore the principal game played with them is very properly and emphatically called 'Hazard.' It requires, indeed, some exertion of the mental powers, of memory, at least, and a turn for such diversions, to play well many games at cards.
Nevertheless, it is often found that those who do so give no further proofs of superior memory and judgment, whilst persons of superior memory and judgment not unfrequently fail egregiously at the card-table.
The gamester of skill, in games of skill, may at first sight seem to have more advantage than the gamester of chance, in games of chance; and while cards are played merely as an amusement, there is no doubt that a recreation is more rational when it requires some degree of skill than one, like dice, totally devoid of all meaning whatever. But when the pleasure becomes a business, and a matter of mere gain, there is more innocence, perhaps, in a perfect equality of antagonists—which games of chance, fairly played, always secure—than where one party is likely to be an overmatch for the other by his superior knowledge or ability.
Nevertheless, even games of chance may be artfully managed; and the most apparently casual throw of the dice be made subservient to the purposes of chicanery and fraud, as will be shown in the sequel.
In the matter of skill and chance the nature of cards is mixed,—most games having in them both elements of interest,—since the success of the player must depend as much on the chance of the 'deal' as on his skill in playing the game. But even the chance of the deal is liable to be perverted by all the tricks of shuffling and cutting—not to mention how the honourable player may be deceived in a thousand ways by the craft of the sharper, during the playing, of the cards themselves; consequently professed gamblers of all denominations, whether their games be of apparent skill or mere chance, may be confounded together or considered in the same category, as being equally meritorious and equally infamous.
Under the name of the Doctrine of Chances or Probabilities, a very learned science,—much in vogue when lotteries were prevalent,—has been applied to gambling purposes; and in spite of the obvious abstruseness of the science, it is not impossible to give the general reader an idea of its processes and conclusions.
The probability of an event is greater or less according to the number of chances by which it may happen, compared with the whole number of chances by which it may either happen or fail. Wherefore, if we constitute a fraction whereof the numerator be the number of chances whereby an event may happen, and the denominator the number of all the chances whereby it may either happen or fail, that fraction will be a proper designation of the probability of happening. Thus, if an event has 3 chances to happen, and 2 to fail, then the fraction 3/5 will fairly represent the probability of its happening, and may be taken to be the measure of it.
The same may be said of the probability of failing, which will likewise be measured by a fraction whose numerator is the number of chances whereby it may fail, and the denominator the whole number of chances both for its happening and failing; thus the probability of the failing of that event which has 2 chances to fail and 3 to happen will be measured by the fraction 2/5.