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. The fractions which represent the probabilities of happening and failing, being added together, their sum will always be equal to unity, since the sum of their numerators will be equal to their common denominator. Now, it being a certainty that an event will either happen or fail, it follows that certainty, which may be conceived under the notion of an infinitely great degree of probability, is fitly represented by unity.