By which it will be 164 to 147 the field against A, (something more than 39 to 35). Now, if we compare this with the last example, we may conclude it to be right; for if it had been 40 to 35, then it would have been 8 to 7, exactly as in the last example. But, as some persons may be at a loss to know why the numbers 39 and 35 are selected, it is requisite to show the same by means of the Sliding Rule. Set 164 upon the line A to 147 upon the slider B, and then look along till you see two whole numbers which stand exactly one against the other (or as near as you can come), which, in this case, you find to be 39 on A, standing against 35 on the slider B (very nearly). But as 164/311 and 147/311 are in the lowest terms, there are no less numbers, in the same proportion, as 164 to 147,--39 and 35 being the nearest, but not quite exact.
Example IV. There are four horses to start for a sweepstake, namely, A, B, C, D, and they are supposed to be as equally matched as possible.
Now, Mr Sly has laid 10 guineas A against C, and also 10 guineas A against D. Likewise Mr Rider has laid 10 guineas A against C, and also 10 guineas B against D. After which Mr Dice laid Mr Sly 10 guineas to 4 that he will not win both his bets. Secondly, he laid Mr Rider 10 guineas to 4 that he will not win both his bets.
Now, we wish to know what Mr Dice"s advantage or disadvantage is, in laying these two last-mentioned wagers.
First, the probability of Mr Sly"s winning both his bets is 1/3 of 14 guineas; and Mr Dice"s expectation is 2/3 of 14 guineas, or L9 16s., which being deducted from his own stake (10 guineas), there remains 14s., which is his disadvantage in that bet.
Secondly, Mr Rider"s expectation of winning his two bets is 1/4, and, therefore, Mr Dice"s expectation of the 14 guineas, is 3/4, or L11 0s.
6d., from which deduct 10 guineas (his own stake), and there remains 10s. 6d., his advantage in this bet,--which being deducted from 14s.
(his disadvantage in the other), there remains 3s 6d., his disadvantage in paying both these bets.
These examples may suffice to show the working of the system; regular tables exist adapted to all cases; and there can be no doubt that those who have realized large fortunes by horse-racing managed to do so by uniformly acting on some such principles, as well as by availing themselves of such "valuable information" as may be secured, before events come off, by those who make horse-racing their business.
The same system was applied, and with still greater precision, to c.o.c.k-fighting, to Lotteries, Raffles, Backgammon, Cribbage, Put, All Fours, and Whist, showing all the chances of holding any particular card or cards. Thus, it is 2 to 1 that your partner has not one certain card; 17 to 2 that he has not two certain cards; 31 to 26 that he has not one of them only; and 32 to 25 (or 5 to 4) that he has one or both--that is, when two cards are in question. It is 31 to 1 that he has three certain cards; 7 to 2 that he has not two; 7 to 6 that he has not one; 13 to 6 that he has either one or two; 5 to 2 that he has one, two, or three cards; that is, when three cards are in question.
With regard to the dealer and his partner, it is 57,798 to 7176 (better than 8 to 1) that they are not four by honours; it is 32,527 to 32,448 (or about an even bet) that they are not two by honours; it is 36,924 to 25,350 (or 11 to 7 nearly) that the honours count; it is 42,237 to 22,737 (or 15 to 8 nearly) that the dealer is nothing by honours.(55)
(55) Proctor, The Sportsman"s Sure Guide. Lond. A.D. 1733.
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."
Founded on this theory we have the following precepts for gamesters:--
1. "For gaming, prefer Roulette, because it presents several ways of staking your money(57)--which permits the study of several.
(57) "Pair, impair, pa.s.se, manque, and the 38 numbers of the Roulette, besides the different combinations of POSITION" and "maturities"
together.
2. "A player should approach the gaming table perfectly calm and cool--just as a merchant or tradesman in treaty about any affair.
If he gets into a pa.s.sion, it is all over with prudence, all over with good luck--for the demon of bad luck invariably pursues a pa.s.sionate player.
3. "Every man who finds a pleasure in playing runs the risk of losing.
4. "A prudent player, before undertaking anything, should put himself to the test to discover if he is "in vein"--in luck. In all doubt, you should abstain."
I remember a curious incident in my childhood, which seems much to the point of this axiom. A magnificent gold watch and chain were given towards the building of a church, and my mother took three chances, which were at a very high figure, the watch and chain being valued at more than L100. One of these chances was entered in my name, one in my brother"s, and the third in my mother"s. I had to throw for her as well as myself. My brother threw an insignificant figure; for myself I did the same; but, oddly enough, I refused to throw for my mother on finding that I had lost my chance, saying that I should wait a little longer--rather a curious piece of prudence for a child of thirteen. The raffle was with three dice; the majority of the chances had been thrown, and 34 was the highest. After declining to throw I went on throwing the dice for amus.e.m.e.nt, and was surprised to find that every throw was better than the one I had in the raffle. I thereupon said--"Now I"ll throw for mamma." I threw thirty-six, which won the watch! My mother had been a large subscriber to the building of the church, and the priest said that my winning the watch for her was quite PROVIDENTIAL. According to M. Houdin"s authority, however, it seems that I only got into "vein"--but how I came to pause and defer throwing the last chance, has always puzzled me respecting this incident of my childhood, which made too great an impression ever to be effaced.
5. "There are persons who are constantly pursued by bad luck. To such I say--NEVER PLAY.
6. "Stubborness at play is ruin.
7. "Remember that Fortune does not like people to be overjoyed at her favours, and that she prepares bitter deceptions for the imprudent, who are intoxicated by success."
Such are the chief axioms of a most experienced gamester, and M. Houdin sums up the whole into the following:--
8. "Before risking your money at play, you must deeply study your "vein"
and the different probabilities of the game--termed the maturity of the chances."
M. Robert-Houdin got all this precious information from a gamester named Raymond. It appears that the first meeting between him and this man was at a subscription-ball, where the sharper managed to fleece him and others to a considerable amount, contriving a dexterous escape when detected. Houdin afterwards fell in with him at Spa, where he found him in the greatest poverty, and lent him a small sum--to practise his grand theories as just explained--but which he lost--whereupon Houdin advised him "to take up a less dangerous occupation." He then appears to have revealed to Houdin the entertaining particulars which form the bulk of his book, so dramatically written. A year afterwards Houdin unexpectedly fell in with him again; but this time the fellow was transformed into what he called "a demi-millionnaire," having succeeded to a large fortune by the death of his brother, who died intestate. According to Houdin the following was the man"s declaration at the auspicious meeting:--"I have," said Raymond, "completely renounced gaming. I am rich enough, and care no longer for fortune. And yet," he added proudly, "if I now cared for the thing, how I could BREAK those bloated banks in their pride, and what a glorious vengeance I could take of BAD LUCK and its inflexible agents! But my heart is too full of my happiness to allow the smallest place for the desire of vengeance."
A very proper speech, unquestionably, and rendered still more edifying by M. Houdin"s a.s.surance that Raymond, at his death three years after, bequeathed the whole of his fortune to various charitable inst.i.tutions at Paris.
With regard to the man"s gaming theories, however, it may be just as well to consider the fact, that very many clever people, after contriving fine systems and schemes for ruining gaming banks, have, as M. Houdin reminds us, only succeeded in ruining themselves and those who conformed to their precepts.
Et s"il est un joueur qui vive de son pain, On en voit tous les jours mille mourir de faim.
"If ONE player there be that can live by his gain, There are thousands that starve and strive ever in vain!"
CHAPTER IX. THE HISTORY OF DICE AND CARDS.
The knights of hazard and devotees of chance, who live in and by the rattle of the box, little know, or care, perhaps, to whom they are indebted for the invention of their favourite cube. They will solace themselves, no doubt, on being told that they are pursuing a diversion of the highest antiquity, and which has been handed down through all civilized as well as barbarous nations to our own times.
The term "cube," which is the figure of a die, comes originally from the Arabic word "ca"b," or "ca"be," whence the Greeks derived their cubos, and cubeia, which is used to signify any solid figure perfectly square every way--such as the geometrical cube, the die used in play, and the temple at Mecca, which is of the same figure. The Persic name for "die" is "dad," and from this word is derived the name of the thing in Spanish, Portuguese, and Italian, namely, dado. In the old French it is det, in the plural dets; in modern French de and dez, whence our English name "die," and its plural "dies," or "dice."
Plato tells us that dice and gaming originated with a certain demon, whom he calls Theuth, which seems very much like the original patronymic of our Teutonic races, always famous for their gambling propensity.
The Greeks generally, however, ascribed the invention of dice to one of their race, named Palamedes, a sort of universal genius, who hit upon many other contrivances, among the rest, weights and measures. But this worthy lived in the times of the Trojan war, and yet Homer makes no mention of dice--the astragaloi named by the poet being merely knuckle-bones. Dice, however, are mentioned by Aristophanes in his comedies, and so it seems that the invention must be placed between the times of the two poets, that is, about 2300 years ago. At any rate the cube or die has been in use as an instrument of play, at least, during that period of time.
The great antiquity, therefore, of the die as an instrument of pastime is unquestionable, and the general reason a.s.signed for its invention was the amus.e.m.e.nt and relaxation of the mind from the pressure of difficulties, or from the fatigues and toils of protracted war. Indeed, one conjecture is, that gaming was invented by the Lydians when under the pressure of a great famine; to divert themselves from their sufferings they contrived dice, b.a.l.l.s, tables, &c. This seems, however, rather a bad joke.
The afflicted Job asks--"Can a man fill his belly with the east wind?"
And we can imagine that plenty of tobacco to smoke and "chaw" would mitigate the pangs of starvation to an army in the field, as has been seriously suggested; but you might just as well present a soldier with a stone instead of bread, as invite him to amuse himself with dice, or anything else, to a.s.suage the pangs of hunger.
Be that as it may, time soon matured this instrument of recreation into an engine of destruction; and the intended palliative of care and labour has proved the fostering nurse of innumerable evils. This diminutive cube has usurped a tyranny over mankind for more than two thousand years, and continues at this day to rule the world with despotic sway--levelling all distinctions of fortune in an instant by the fiat of its single turn.