Light Come, Light Go: Gambling—Gamesters—Wagers—The Turf

by Ralph Nevill

In any game, for instance, equality in play is likely to restore the players in a series of events to the same state in which they began; while inequality, however small, has a contrary effect, and the longer the game be continued, the greater is likely to be the loss of the one player and the gain of the other. As has been very soundly said, this "more or less," in play, runs through all the ratios between equality and infinite difference, or from an infinitely little difference till it comes to an infinitely great one. The slightest of advantages, whether arising from skill or chance, will as surely "materialise" in the course of play as does the carefully calculated profit of a commercial expert.

An event either will happen or will not happen; this constitutes a certainty. Some events are dependent, others independent. The difference is very important. Independent events have no connection, their happenings neither forwarding nor obstructing one another. Choosing a card from each of two distinct packs includes two independent events; for the taking of a card from the first pack does not in any way affect the taking of a card from the second—the chances of drawing, or of not drawing, any particular card from the second pack being neither lessened nor increased. On the other hand, the taking of a second card from a pack from which one has already been drawn is a dependent event, as the composition of the pack has been altered by the abstraction of one particular card.

The surprising way in which an apparently small advantage operates may be judged from the following example:—A and B agree to play for one guinea a game until one hundred guineas are lost or won. A possesses an advantage on each game amounting to 11 chances to 10 in his favour. Mathematical analysis of this advantage proves that B would do well to give A upwards of ninety-nine guineas to cancel the agreement.

Further, many speculative events, which at first sight seem to be advantageous to one side, are demonstrated by mathematical investigation to be of an exactly contrary nature. A bets B thirty-two guineas to one that an event does not happen, and also bets B thirty guineas even that it does happen in twenty-nine trials. Besides this A gives B one thousand guineas to play in this manner six hours a day for a month. Here B would appear to have some advantage. Mathematical investigation, however, proves that in reality the advantage of A is so great that B ought not only to return the thousand guineas to A, but give him, in addition, another ten thousand guineas to cancel the agreement.

Every game of chance presents two kinds of chances which are very distinct—namely, those relating to the person interested (the player) and those inherent in the combinations of the game. That is to say, there is either "good luck" or "bad luck," which at different times gives the player a "run" of good or bad fortune. But besides this, there is the chance of the combinations of the game, which are independent of the player and which are governed by the laws of probability. Theoretically, chance is able to bring into any given game all the possible combinations; but it is a curious fact that there are, nevertheless, certain limits at which it seems to stop. A proof of this is that a particular number at roulette does not turn up ten or a dozen times in succession. In reality there would be nothing astounding about such a run, but it is supposed never to have happened. On the other hand, the numbers in one column at roulette have been known not to turn up during seventeen successive coups.

All the same, extraordinary runs do occur at all games. In 1813, a well-known betting man of the name of Ogden laid one thousand guineas to one guinea, that calling seven as the main, a player would not throw that number ten times successively from the dice-box. Seven was thrown nine times in direct sequence! Mr. Ogden then offered four hundred and seventy guineas to be let off the bet, but the thrower refused. He took the box again but threw only twice more—nine—so that Mr. Ogden just saved his thousand guineas.

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 coup. It would almost appear, in fact, as if there existed an instant, prescribed by some unknown law, at which the chances become mature, and after which they begin to tend again towards equalisation. This is the secret of the pass and the counter-pass, and also of the strange persistence which certain numbers at roulette sometimes show in recurring—they are merely making up for lost time. At the end of a year all the numbers on a roulette board would be found to have come up about the same number of times—provided, of course, that the wheel is kept in proper working order, a state of affairs which is assured at Monaco by scrupulous daily inspection.

The considerations set forth above apply more especially to games like roulette and trente-et-quarante played at public tables, where all players have an equal chance against the bank, and where the personal element, which is so important in private play, is to a large extent eliminated. It is at public tables that the real gambler finds his best chance. There, whilst having a fair field and no favour, he may, if lucky, win very large sums with the certainty of being immediately paid; and he is not exposed to various unfavourable influences, which tell against men of his disposition when gambling amongst acquaintances and even friends. Wherever a number of careless, inattentive people possessed of money chance to be assembled, a few wary, cool, and shrewd men will be found, who know how to conceal real caution and design under apparent inattention and gaiety of manner; who push their luck when fortune smiles and refrain when she changes her disposition; and who have calculated the chances and are thoroughly master of every game where judgment is required.

Occasionally men of this stamp have been known to have accumulated a fortune, more often a respectable competency, at play. If they had been interrogated as to the exact means by which they had made their success, they would, had they been desirous of speaking the truth, have replied in the words of the wife of the Maréchal d'Ancre, who, when she was asked what charm she had made use of to fascinate the mind of the queen, "The charm," she replied, "which superior abilities always exercise over weaker minds."