1stly, (13+12+11+10+9+8+7+6x5): 85 -13+12+11+10+9+8+7+6+5), or 81: 4.

(2dly, (13+12+11+10+9+8+7+6):85-(13

+12+11+10+9+8+7+6+5), or 76 : 4.

Viz. where the point is 39, it is 204 : 1, that he do not lose and 19: 1, that he win.

And, where the point is 40, it being evident that the player cannot lose, we find, (13+12+ 11+10+9+8+7+6+5):85−(13+12+11+10 +9+8+7+6+5+4), or 81: 1, that he win.

From these data may be deduced, as a matter of curiosity, the just proportions which the banker may give or receive by composition for the monies ventured upon the knowledge of the first point.

Of course, the compositions here spoken of are only to be made from the proportions established above, as long as the cards for Noir are alone played; for were any cards for the opposite colour already appearing, the situation of the game would be altered. And this leads us to observe, that the last card of the talon or pack ought not to count, because it is known; and as we may speculate on the last coup, the equality of the game would be destroyed from this circumstance, that whenever the last coup finishes with the last card, it is almost always probable that Rouge will win; for by reference to the calculation in page 1, it is evident that there are a greater number of last cards capable of furnishing a low than a high coup.

From the observations above it must be obvious, that there exists no means for winning with certainty, or even for diminishing the slightest portion of the banker's advantage. In the long run, events are balanced, and the banker having more chances in his favour than the player has,

Thus, if a

the former must necessarily win. player has been fortunate enough to win a considerable sum on one coup, it will dwindle away in detail; and, vice versa, what he had won in detail, à la martingale, he would lose en gros; for this reason that of whatever number of coups the martingale may be composed, it will break in a proportion equal to what it may produce.

The number of combinations that may be composed in a series of 26 coups is immense. There are no less than 67108864 different ways in which a taille consisting of 26 coups may happen.

Thus, whatever way we may determine on, there are (67108864-1) other ways, all equally possible. In this number there is but one chance for Noir winning, and one chance for Rouge; one that there may be no interruption commencing with Noir, and one that there may be no interruption commencing with Rouge. It is possible that by dint of tailles these events may sometimes occur; but the period in which we may reasonably look for them is too long; for supposing 10 tailles per diem, it would require a space of 18500 years to see them once happen.

If a player has had the good fortune to double, triple, or quadruple his martingale, we must not imagine that his system of play is better than another, since it is in reality but the same degree of luck as the winning of a paroli et sept et le va, seven times the original stake.

Every progression comes to the same thing; and that which increases the most is nothing more than deeper play. He who imagines that he is only staking a sovereign because the first coup of his martingale commenced with that snm, is in reality playing more deeply than he conceives;

for instance, if the martingale has run 6 coups, and that it amounts to 120 sovereigns every coup, one with another, will amount to 5 sovs.; so that if without donbling he had played each coup 5 sovereigns, it would have come to the same thing, and in the long run, he would lose as much one way as the other. This does not, however, exclude the possibility of winning momentarily, because in a small number of coups the advantage of the banker is comparatively trifling, but in the long run, the player will pay dearly for his amusement; and we hope that the mathematical analysis which we have given of this game, which holds the first rank in the gaming-houses of Europe, will convince the most sceptical of our readers of the impossibility of combining any system for winning, and put them upon their guard against those designing knaves ever on the alert to entrap the unwary by the glittering temptation of a system which they impudently assert requires but the risk of a small capital to gain millions.

EXPLANATION OF THE TERMS USED AT ROUGE ET

NOIR.

BANQUIER. The dealer.

FAUSSE TAILLE. Is when the dealer commits a fault, which subjects him to double all the money staked.

MARTINGALE. A mode of play which consists in staking double the amount of the money lost. PAROLI. Double the sum staked the first time.

REFAIT DE TRENTE ET UN. A coup by which the banker wins one half the money staked, and is effected by dealing 31 for each colour.

REFAIT. Is when the banker deals the same sum for both colours from 32 to 40.

SEPT ET LE VA. Seven times the amount of the sum first staked.

TAILLE.

Is made when the banker has dealt out all the cards.

FIGURE. The name given to the kings, queens, and knaves.

POINT. The number which results from the sums of the cards dealt by the banker.

NOIR. The colour for which the first points are dealt by the banker.

ROUGE. The colour for which the banker deals the points after those for black.

BANKER. The dealer.

PUNTER. Those who play against the banker.

LA ROULETTE.

THE form of the table used for this game is an oblong square, covered with green cloth, in the centre of which there is a round cavity, around the sides of which, equidistant one from the other, are ranged several bands of copper, which commencing at the top, descend just to the extremity of the machine. In the centre of this cavity, which is moveable, is formed a circular bottom, containing 38 holes, to which the copper bands are attached, and upon which are painted, alternately in black and red, 36 numbers, from 1 a 36 a zero (0) and a double zero (00).