Hoyle's Games Modernized/Trente et Quarante

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By Captain Browning.

Trente et Quarante is played with six packs of cards on a table marked out as in the illustration (Fig. 3); this represents one-half of the table, the other half being marked out in an exactly similar manner. There are but four chances—Rouge, Noir, Couleur, and Inverse, which are played on in the following manner. The six packs of cards, having been well shuffled, are cut, and so many cards dealt out face upwards in a row until the sum of the pips (Aces, Kings, Queens, Knaves, and tens counting ten each, and the Ace one) exceeds 30 in number. Then a second row is dealt out in a similar manner, below the first one, until the number of the pips in this second row also exceeds 30. The top row is called "Black," the second or underneath row "Red," and the Red or Blacks win according to which row contains the fewer number of pips—e.g. whichever row of cards adds up nearest to 30.

The number to which each row adds up is called "the point," and it will be plain that the best point possible is 31, and the worst point possible 40. It is customary, when calling out the "point" of Black and Red to drop the "thirty" and say simply 2 and 6, which would mean that the point of Black amounts to 32, and the point of Red 36, in which case the Black or top row would win. The Black "point" is always called out first.

Fig. 3.

Fig. 3.

The other chance, the Couleur and Inverse, is decided by the colour of the first card turned up. If the colour of this card corresponds with the colour of the winning row, then Couleur wins; if it is of the opposite colour, then Inverse wins. Thus suppose the top or Black row of cards amounts to 35, and the first card in this row is a Black card, and the Red row amounts to 36, then Black and Couleur would win; had the first card in the Black row been a Red card, then Inverse would have won, being of the opposite colour to the winning row (Black).

The players wishing to back any particular chance place their stakes on that portion of the table reserved for Black, Red, Couleur, or Inverse, as shown in the illustration (Fig. 3). There are two chefs-de-parties employed to supervise the game, and four croupiers to receive the losing stakes and pay the winning ones, one of the croupiers also being the tailleur, or dealer of the cards. The tailleur calls the game by saying, "Messieurs, faites vos jeux," when the players stake on the different chances. He then says, "Les jeux sont fait. Rien ne va plus," after which no further stakes may be made. He then deals out the cards, and when both rows are complete he calls the result thus, "Deux, six, Rouge perds et Couleur gagne," or "Rouge perds et Couleur," as the case may be, meaning that the point of Black is 32 and that of Red 36, so that Black and the colour win; or Black wins and the colour loses. It should be noted that the "tailleur" never mentions the words "Black" or "Inverse," but always says that Red wins or Red loses, and that the colour wins or the colour loses. On the conclusion of each coup both rows of cards are swept into a small basket called the "talon," which is let into the centre of the table, and the game begins again. When the six packs of cards are exhausted, the "tailleur" says, "Monsieur, les cartes passent," when all the cards are collected out of the talons, re-shuffled and cut, and a fresh deal is started.

All four chances—Red, Black, Couleur, and Inverse—are of course even chances, and are paid as such by the Bank; but should the total (or point) of both rows of cards be exactly 31 each, the same procedure occurs as upon the appearance of the zero at Roulette—that is to say, the stakes are put en prison; then another deal is made, and those stakes which are on the winning chances are allowed to be withdrawn by the players. Or, as at Roulette, the stakes, at the players' option, may be halved with the Banker in the first instance.

Saving 31, all other identical points made by the Red and Black cause that deal to be null and void, the player being at liberty to remove his stake or otherwise, as he chooses. The condition of affairs (both rows coming to 31 each) which corresponds to the Roulette zero is called a "Refait," and is announced, as are all other identities of the points, by the word "après." Thus suppose the Black row counts up to 38, and the Red row to the same figure, the tailleur announces "Huit, huit après." If it happens to be a Refait, he says, "Un, un après," and the stakes are put into prison.

The Refait is said to occur once in 38 deals on the average; and if this were true, the Bank would have a slightly less advantage at Trente et Quarante than it has at Roulette. To arrive at the mathematical odds in favour of the Bank would involve an exceedingly complicated calculation, and it is doubtful if they have ever been exactly computed. At a glance it would seem that the odds against both rows being 31 each is 81 to 1; there being 10 possible points for each row, the chances against any named point appearing would seem to be 9 to 1, in which case, of course, the chances against both points being identical would be 9 × 9, or 81 to 1. But as the point of 31 can be formed in 10 ways—for the last card may be of any value, while the point of 32 can only be formed in 9 ways—for now the last card cannot be an ace; and to form a point of 33 the last card can be neither an ace nor a deuce, and so on with every point up to 40, which can only be formed in one way—viz. when the last card is a 10—it is obvious that 31 is the easiest possible point to arrive at, and the exact chances against its formation have, as far as the writer's information goes, never been calculated.[111]

In actual play, however, the punter may insure against the Refait by paying a premium of 1 per cent. on his stake (at a minimum cost of five francs); thus it is safe to assume that for all practical purposes the percentage in favour of the Bank is exactly 2 percent.[112] Thus it would seem that once in 38 is an underestimate of the appearance of a Refait.

The maximum and minimum stakes allowed at Trente et Quarante are 12,000 francs and 20 francs respectively. Much heavier amounts are to be seen at stake at this game than at Roulette. This probably arises from two facts: because the games are generally carried out in a quieter manner and the coups are more quickly played than is the case at Roulette, and because there is unquestionably a prevailing idea amongst the gamblers at Monte Carlo that the Bank's advantage is not so great at Trente et Quarante as it is at Roulette. The latter consideration is probably wrong; and, as far as the writer's experience goes, it is a very paying business to insure the stake at Trente et Quarante. If this really is so, it follows that the percentage in favour of the Bank is over 2 per cent., or something like 1 per cent. more than it is at Roulette.

Any system that is applicable to the even chances at the Roulette table can of course be played at Trente et Quarante; but for some reason or other it is unusual to see any system properly worked at this game, possibly because too large a capital would be required.

The almost universal method of play is to follow the "tableau"—that is, to follow the pattern of the card on which the game is marked. If there have been two Reds followed by two Blacks, ninety-nine people out of a hundred will stake on Red, in the expectation of two Reds now appearing, while if there is a run of one colour, thousands of francs will be seen on that colour, and not a single 20-franc piece on the other. Sometimes the colours do run in the most inexplicable manner at Trente et Quarante. The writer has played at a table where there were 17 consecutive Blacks, then 1 Red, to be followed by 16 consecutive Blacks. When such runs occur, the Banks of course lose heavily, and are constantly broken. To break the Bank in the true sense of the word is of course an impossibility. When a Bank gets into low water the chef-de-partie sends for some more money, which is "Ajouter à la banque," and to this extent only is it possible to "break the Bank at Monte Carlo."

The game of Trente et Quarante is sometimes called "Rouge et Noir."


The method of play on the even chances that will now be explained is based on the three following assumptions:—

First. That every system at present played is successful only for a certain time, when an adverse run, long enough to defeat the progression adopted, is almost certain to occur, whereby the Bank reaps a rich harvest.

Secondly. That only on rare occasions does the system show the desired profit, without the player having been at some period of the game a very heavy loser.

Thirdly. That the failure of systems is not due to zero, but to the Bank's maximum.

These conditions are assumed, though in the first two cases they undoubtedly are realities, and within the experience of every system player. The third one may be true or not; it is not vastly important.[113]

Now as regards maxim No. 1, it may be taken for granted that for all practical purposes the system player makes his "grand coup"[114] on not more than (say) twenty occasions, and on the twenty-first he meets such an adverse run that he loses his entire profits plus his entire capital; or say, for argument, he had already spent his profits and so loses only his entire capital. The proportion of the coup played for to the capital employed is generally some 2½ per cent.; consequently after twenty good days' play, and one bad one, a system player is a loser of 50 per cent. of his money. (This is a very low estimate.)

Now supposing a player had played stake for stake on the opposite chance to that played on by the system player, it is obvious that he would have lost on twenty days, and won on the twenty-first sufficient to recoup all his previous losses, with 50 per cent. profit.

The mathematician will say "No" to this—"the Bank will have reaped its zero percentage from each spin of the Wheel during the progress of the play." But why? A, who is playing the system, stakes 10 louis on Red; B (who is playing against him) stakes 10 louis on Black, and zero crops up. They are both put in prison, and A comes out safely, so B is now 10 louis worse off than A. But in a short time A and B again both stake 10 louis, and zero appears. But this time B comes out safely, in which case A must write this down as a losing coup, and his next stake will be say, for example, 15. To meet this B has only to add 5 louis to the 10 he has just retrieved out of prison—so his profit and loss account due to zero is exactly square, as far as it affects his transactions with A. And surely during the course of a game A and B will both get out of prison the same number of times. (And A does not fear zero—he only fears reaching the maximum—consequently B does fear for zero; he but awaits the time when his stake gets to the maximum.)

Is it not desirable to be B? He requires no capital—or very little—and yet is in a position to win all that A is eventually going to lose—as he most certainly must lose. To play on this method is exceedingly simple. All that has to be done is to take any system, and play it in reverse order to what it is designed to be played in. The effect of this is, in a word, to compel the Bank to play this system in its correct order against the punter. The writer has always employed a Labouchere to play on this method, and it is the simplest one by which to explain the procedure.

A reference to p. 456 will show that the Labouchere system, is played by writing down so many figures, so that their sum amounts to the grand coup—or stake being played for—and that it is usual to write down the figures 1, 2, 3, 4; so that the grand coup is 10 units. To play this system in the usual manner it is generally assumed that a capital of 400 or 500 units is required. By reversing matters in play the first important advantage gained to the player is that he needs but a capital of 10 units, and his grand coup becomes 400 or 500 units. Very well. The figures 1, 2, 3, 4 are written down, and the first stake is the sum of the extreme figures—5. This sum is lost; but now the 5 is not written down after the 4, but the 1 and the 4 are erased. The next state is again 5 (2 + 3), and is again lost, the 2 and 3 are erased and the player retires. Suppose this second stake of 5 had been won, then instead of erasing the 2 and 3, the figure 5 would be written down on the paper, so the row would read 1, 2, 3, 4, 5, and the next stake would be (5 + 2) 7. Should this be lost the 5 and 2 are erased, the next stake being 3. Suppose it is won, this figure is written down, and the row now reads 1, 2, 3, 4, 5, 3, and the next stake is 3 + 3 (6), and so on. But the moment all figures are erased, the player will have lost 10 units and must retire. This he will have to do a great many times, but finally such a run as the following will occur. The Red is staked on throughout—the dot indicating which colour wins.

Figures. Stake. R. B. + or –
1 01 + 4 005 –5
2 02 + 3 005 • +0
3 02 + 5 007 • +7
4 02 + 7 009 • +16
5 02 + 9 011 • +27
7 02 + 11 013 +14
9 03 + 9 012 +2
11 05 + 7 012 • +14
12 05 + 12 017 • +31
17 05 + 17 022 • +53
22 05 + 22 027 • +80
27 05 + 27 032 +48
07 + 22 029 +19
29 12 + 17 029 • +48
41 12 + 29 041 • +89
12 + 41 053 +36
46 17 + 29 046 • +82
17 + 46 063 +19
29 29 029 • +48
58 29 + 29 058 • +106
87 29 + 58 087 • +193
29 + 87 116 +77
87 29 + 58 087 • +164
29 + 87 116 +48
58 058 58 • +106
116 58 + 58 116 • +222
174 58 + 116 174 • +396
232 58 + 174 232 • +628
290 58 + 232 290 • +918

This shows a run of 29 coups, of which the player wins 20 and loses 9.

He is 918 units to the good, and his next stake would be 348![115]

Assuming a player had been working a Labouchere on this run in the usual manner, on Black with a capital of 500 units, he would have had to retire after the 27th coup through lack of capital; and assuming him to have been playing with a 20-franc unit, he would have had to retire from Roulette on the 28th coup, and from Trente et Quarante after a few more coups if the bad sequence continued, no matter how large his capital had been.

It has been stated that the Bank beats the system player only on account of its limit. This is not quite true; it has also one more great advantage over the player, and this is the fact of its being a machine, while the punter is human; and although a player will stake his all to retrieve his previous losses, he will not—nature will not allow him to—risk his winnings to win still more.

This is a psychological fact that cannot be explained. It must be to the knowledge of most people who have visited Monte Carlo, that a player will stake as much as 500 francs to retrieve a loss of a single 5-franc piece. Yet the same player, having turned a 5-franc piece into as little as 50 francs, will refuse to adventure another stake, and retire from the gaming-table. When the player is having his bad run, the Bank cannot help playing their winnings to the maximum stake—they must do so; but the player on his good run is not compelled to play up his winnings, and really cannot be expected to do so. Theoretically he should, and I firmly believe there is a lot of money awaiting the player who has the patience to wait for such a run—which must come to him, equally as it must and does, we know, come to the Bank—and then play on and on until he is prohibited by the Bank from staking any higher. To play a system upside-down, or in reverse order, requires great patience and equanimity, until the favourable run occurs, when indomitable pluck and perseverance are the necessary qualifications.

The writer feels bound to take the reader into his confidence so far as to acknowledge that he himself has never had such pluck, but has always retired on winning between 200 and 300 units. But he has always watched the future run of the table, and on no less than five occasions would have reached the maximum stake and won over 1000 units. He has, however, always had the patience, and lost his petit coup time after time with perfect equanimity, and only wishes he had had the other qualifications as well.

Referring for one moment to the assumed fact No. 2 on which this method is based—that a player more often than not is in deep water before bringing off his grand coup; which he must be, owing to the losses being so disproportionate in magnitude to the gains—it might be a good plan to discover what the average highest loss of a system player is before the system shows a profit, and then to play the same system in reverse or upside-down order, making this figure the grand coup. Playing in this manner, a visitor will have a cheap and enjoyable visit to Monte Carlo, and may be assured of one of the most exciting little periods of his career when this favourable run of luck does come his way.

One final word of advice to all system players. Play on the chance that is most convenient to your seat at the table. It is as likely to win as any other. Never get flurried with your system or calculations. It is not at all necessary to stake on every coup. You are just as likely to win if you postpone staking until the day after to-morrow, as if you stake on the very next spin of the Wheel—the Rooms are open for twelve hours per diem, which should allow ample time for the number of coups you wish to play.

There may or not be such a thing as "luck." There can, however, be no harm in giving its existence the benefit of the doubt. If on some particular occasions you find you cannot do right, assume you are out of luck, and stop playing. Do not consider either that you owe a grudge to the Bank because you have lost, or that it is absolutely necessary to retrieve your fortune then and there! Postpone playing until the following day, or week, or year, when you may be in good luck, and can easily recoup yourself.

Always bear the clever gambler's great maxim well in mind: "Cut your losses—play up your gains!"


The writer's only object has been to try and explain how the games of chance are played at Monte Carlo, and to point out that the player is at a disadvantage on each occasion that he stakes, though that disadvantage may be increased or reduced by bad or good staking. It now remains for the reader to decide whether the pleasure he derives from gambling is likely to recompense him for his probable losses.

111 ^  A German mathematician is said to have calculated the percentage in favour of the Banks to be 1.28 per cent.

112 ^  It must be remembered that as the player is at liberty to withdraw half his stake when there is a Refait, he is really paying a premium of 1 per cent. to insure only half his stake.

113 ^  If there were no limit every one could win at Monte Carlo, by the simple method of doubling up after each loss. Hence sans maximum, zero does not prevent the Bank from losing.

114 ^  Most system players try to win a percentage of their capital per diem. Having done so, they retire from the table. By "grand coup" is meant this amount of daily winnings. There is no reason why a player should not play his system ad infinitum. He, however, instinctively knows the grave risk he is running by continuing his game, and is generally very pleased to retire after having made a certain daily profit.

115 ^  In the series shown on p. 457, had a player been fortunate enough to have played a "Labouchere reversed" on Black, he would have won 890 units.