Hoyle's Games Modernized/Roulette

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By Captain Browning.

("Slambo" of The Westminster Gazette.)

Fig. 1.

Fig. 1.

The Roulette table, which is covered with a green padded cloth, and marked out as shown in Fig. 1, is divided into two portions, the Roulette, or Wheel as it is commonly called, itself being let into the centre of the table between these two portions.

Fig. 1 is an illustration of one-half of the table, the other half being marked in exactly a similar manner. It will be seen that the cloth is divided into three long columns of figures, marked from 1 to 36. At the bottom end of these columns there are three spaces, representing all the numbers in the first, second, and third column respectively. There are three similar spaces both on the right and on the left, marked 12 D, 12 M, 12 P, indicating the third (Dernière), the second (Milieu), and first (Première) twelve (Douzain) numbers.

On either side of the column of figures are further spaces to mark the Rouge (or Red numbers); Impair (or odd numbers), Manque (all numbers from 1 to 18 inclusive) on the one side; and the Noir (or Black numbers), Pair (or even numbers), and Passe (all numbers from 19 to 36 inclusive) on the other side; at the top of all is the space reserved for zero.

The Roulette, or Wheel, itself (Fig. 2) consists of a narrow circular ledge (A. A.) fixed in the table, and sloping downwards. Within this ledge is a brass cylinder (C. C.), suspended on a pin at its centre, and capable of being made to revolve by means of a cross-head or handle (H. H.).

The outer edge of the brass cylinder is divided into thirty-seven small compartments, numbered in irregular order from 1 to 36, and coloured alternately Red and Black; the 37th compartment being the zero.

The game is played in the following manner. A croupier—styled the Tourneur—calls out, "Messieurs, faites vos jeux," when the players place their stakes on that portion of the cloth which indicates the chance they wish to play upon. The tourneur then says, "Les jeux sont fait," and throws a small ivory ball round the inclined ledge (A. A.) in one direction and turns the cylinder in the opposite direction. When the ball is coming to rest the croupier calls out, "Rien ne va plus," after which no further stakes can be made. As the ball comes to rest it gradually slips down the ledge, and finally lodges in one of the compartments in the cylinder. The number of this compartment is the winning number, and upon its colour, figure, &c., depend the results played for. It is announced by the tourneur in this way, "Onze, noir, impair, et manque," which means that number 11, the Black, the uneven, and the manque (numbers 1 to 18) win. The losing stakes are first raked into the Bank, then the winnings are paid, after which the tourneur again says, "Messieurs, faites vos jeux," and the game proceeds as before.

Fig. 2.

Fig. 2.

There are no less than eight different methods of staking at Roulette. Besides the three even chances: Red, Black; Pair, Impair; Passe or Manque, one single number may be backed. This is called staking en plein. Or two numbers may be coupled (à cheval); or three numbers (transversale pleine); or four numbers (carré); or six numbers (transversale simple, or sixaine). In addition, the first, second, or third dozens of numbers (Douzaine Première, Milieu, or Dernière), and the first, second, or third column each of twelve numbers may be staked upon. The odds offered by the Bank against backing a single number en plein is 35 to 1, and the odds against the other chances in proportion: thus against either of two numbers appearing 17 to 1 is paid; against either of three numbers, 11 to 1; against either of four, 8 to 1, and so on; while obviously against each dozen, or column, 2 to 1 is paid; the Red, Black, Pair, Impair, Passe, or Manque being even money chances.

A player wishing to stake on any of the even chances, or the dozens, or the columns, places his money on the portion of the cloth marked out for that chance. To back a single number, the stake is placed where that number is painted on the cloth; to back both of two numbers, the stake is placed à cheval—that is, on the line between these two numbers. To stake on three numbers with one coin, the amount is placed on the border-line of the outside number of three numbers. Four numbers are backed when the coin is so placed that it touches all four numbers, and six numbers are combined in one bet by placing the stake on the outside of the line dividing these six numbers. Zero may also be staked upon by placing the coin in the zero area; also zero, 1, 2, 3 (quatre premières), by putting the stake on the outside of the line dividing zero from 1, 2, 3; or zero coupled with 1 and 2; or 2 and 3 in a similar manner. In the illustration (Fig. 1) an example is given of staking in all these various ways. It will be noticed that consecutive numbers on the table can only be staked upon in combination, not consecutive numbers on the Wheel. Thus to combine the three voisins, or adjacent numbers, 0, 26, 15 on the Wheel, three separate stakes would be required.

Any two dozens may be combined, or any two columns, by placing the stake on the line between the two; and the player, when successful, receives one-half of the amount risked. Also any two even chances, such as Rouge and Impair, whose position is adjacent on the cloth, may be combined with one stake by placing the coin on the dividing line between the two; the player is paid even money when both events turn up, and he only loses when neither event appears. But to bet on both Passe and Noir or Rouge and Manque at the same time, two separate states would be required.

The maximum stake allowed on the even chances is 6000 francs (£240)—on a single number 180 francs is the highest possible stake; the maximum stakes on the other chances are in proportion—thus 3000 francs on a dozen or column, and 720 francs on a carré of four numbers. In each case the minimum stake is 5 francs, except when two dozens or two columns are combined with one stake, when at least 10 francs must be risked.

Each table is presided over by two chefs-de-partie, who sit on elevated chairs on either side of the Wheel. There are four croupiers, who sit at the Banque (one being the tourneur), whose duty it is to pay out the winners and rake in the losings. In addition, there is a croupier sitting at either end of the table, who looks after the interests both of the players and of the Bank generally.

There being thirty-seven compartments in the Wheel, and as the odds of 35 to 1 only are paid on the winning number, it follows that on all stakes on numbers, or combination of numbers, the Bank has one chance in thirty-seven, or a percentage of slightly under 3 per cent. in its favour.

The percentage in favour of the Bank on all monies staked on the even chances, however, is only one-half of this amount. On the appearance of zero, all the money at stake is swept into the Bank, with the exception of that on zero itself—which is paid at the same rate as any other number—and the amounts on the even chances—Rouge, Pair, Manque, &c.: these stakes are placed on the lines on the outside of the table (see Fig. 1), and are then said to be in prison.

On the next coup, if the stakes happen to be on the winning chance, they are allowed to be withdrawn by the player. The reader will please notice that this is theoretically exactly the same thing as if the punter halved his stake with the Banker, and this he is allowed to do if he chooses. Should two zeros appear consecutively the stakes are placed still further over these lines; they are now doubly in prison, and have to be doubly released therefrom before the player gets his own money back.

Thus it will be seen that, theoretically, once in every thirty-seven spins the Bank wins half of all money staked on the even chances; on which chances, consequently, the Bank may be said to have a percentage of slightly under 1½ per cent. in its favour. This difference in the percentage in favour of the Bank is either unknown to, or totally disregarded by, the great majority of punters at Monte Carlo; but the player, by judicious methods of staking, to a great extent, can despoil the Bank of its higher percentage. An examination of the illustration (Fig. 1) will show that the following are Red numbers, viz. 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, and 36. Thus Impair contains 10 Red numbers, and but 8 Black ones. The first column includes 6; the second column 4; and the third column 8 Red numbers. Thus a player staking on Black and Impair has no less than twenty-eight numbers in his favour, on eight of which he wins both his stakes, and on twenty he neither wins nor loses. Or a punter staking on the third column and Black, is guarded by twenty-six numbers, on four of which (the four Black numbers in column 3) he receives 1½ times his stakes, on eight (the eight Red numbers in column 3) he receives ½ times his stakes, and on the remainder he neither wins nor loses. Similar wagers can of course be made by combining Red and Pair, or the first column and Red, and so on. Now a player wishing to stake on a great many numbers (which is a very frequent occurrence, and is popularly known as "plastering the table"), instead of placing his money on the various transversales, carrés, and en pleins, by which method he loses all his money if zero appears, should rather stake the equivalent amount on Black and Impair, or Red and Pair, which, as explained, covers twenty-eight numbers. By this method he loses only one-half of his money if zero appears. Nothing is more usual than to see a player stake à cheval on two dozens. A more idiotic method of gambling cannot be conceived. The equivalent amounts (supposing the douze P and the douze M are selected) should be staked on Manque, and the transversale of 19 to 24. Now if zero appears half the stake on Manque is saved, but in the former case the entire stake would be lost!

Many similar instances of good and bad staking could be quoted, but the average player at Monte Carlo considers the percentage against him to be so insignificant that it is scarcely worthy of his notice. However, as its insignificance represents a gain of some hundreds of thousands of pounds sterling per annum to the Administration, it should be worthy of a passing thought at any rate.

Nearly every player at Monte Carlo has a system of some sort, generally played on the even chances. There are, however, systems for playing on numbers, dozens, &c., but these for the most part are of the most fantastic and insane order. The writer has actually known a player whose system was to back thirty-five out of the thirty-six numbers, on the principle that, having but two numbers against him, he would be very unlucky not to win one unit per coup!

Hundreds of people play on one particular number after the appearance of some other particular number, and are confident in themselves that, for example, 3 always turns up after 25; or 10 after 0. A very favourite stake is zero et les quatre premiers—that is, zero en plein, and zero coupled with 1, 2, 3. Another very general stake is les voisins de zéro—or zero and the numbers on either side of it on the Wheel. This is a simple bet to make by putting one coin à cheval between 0 and 3, one between 32 and 35, and one each on 26 and 15. The underlying idea of these zero bets is that the Bank cheats; that it wants zero to turn up; and that the tourneur is skilful enough to throw zero when he wishes. A more ridiculous assumption could not be made—in the first place, because the tourneur cannot throw the ball even to a particular section of the Wheel, much less into zero itself; and in the second place, because the gambling could not possibly be carried out in a more straight-forward manner than it is by the Administration at Monte Carlo. If the tourneur could throw the ball into any compartment he chose, he could, through his friends, ruin the Bank whenever he wished.

If I had space I could tell a story of how M. Blanc offered to give a certain player a year's practice at spinning the Wheel, and then to allow him to be his own croupier and stake as he chose. This is a fact; and yet I have often heard the following class of whispered conversation in the rooms: "Now's our time—there's a lot of money on the even chances—wait till the ball is spun and then bet on zero."

Some players back their age, when not too old—an eventuality that can occur only to the sterner sex. A sweet and blushing maiden of some fifty summers may be observed always to place her stake on No. 28—"Because it's my age, my dear, and to-day is my birthday!" Others back the number of their cloak-room ticket, or the number of the hymn for the day (if they should happen to have been present at church to hear it sung)—indeed everybody has a pet number; and why not? One number is just as likely to appear as any other. These are not systems in the true sense of the word, but they constitute a systematic method of staking, which is always advisable for play—be they ever so weird and fantastic—as they keep the player within certain limits, and prevent him from losing his head, and making wild plunges to retrieve all his losses by one lucky spin of the Wheel.

The more business-like systems are played on the even chances. Many are exceedingly ingenious, and on paper would appear certain to "break the Bank at Monte Carlo!"

The underlying principle of all such systems is to play a Martingale—that is, after each loss to increase the stake in various proportions until all previous losses have been recouped, and a profit is shown. The commonest and simplest to play is the "Montant et demontant," which consists in increasing the stake after a loss by one unit per coup until the player is one unit to the good. Thus if the first stake be lost, the next stake would be two units, which is also lost, as is the next one of three units. The player would now have lost six units in all. His next stake becomes 4, which, supposing it to be won, would leave him a net loser of two units. The stake would now be dropped to three units; for the object is to be but one unit to the good. Should this stake win, the game would be started all over again with one unit. On the other hand, if the 3 had been lost, the next stake would be 4, and so on. There are many other systems. The general principle of them all is exactly the same; the calculations and paper results being nothing more nor less than an ingenious method of juggling with figures.

The Fitzroy system aims at winning one unit per coup played. For the working of this system it is necessary to keep a column in which imaginary losses are written down: the player assuming that he loses one unit more and wins one unit less than he actually does. The stakes are increased by unity as in the "Montant et demontant" system, with the exception of the second stake, which (after a loss) is three instead of two units, until the imaginary losses column comes out clear. Here is an example of ten coups played on the Fitzroy system:—

Stake. W.
or L.
+ or –
Stake. W.
or L.
+ or –
1 L.1 –1 –2 6 W.6 –3 –9
3 L.3 –4 –6 7 W.7 +4 –3
4 W.4 00 –3 4 L.4 –0 –8
4 L.4 –4 –8 5 W.5 +5 –4
5 L.5 –9 –14 5 W.5 +10 ±0

Showing ten units won for ten coups played, the imaginary loss column now reading ±0.

Another very ingenious scheme is that known as the "Labouchere" system. To play this so many figures are written down that their total equals the "grand coup"[109] that is being played for. Ten is the customary coup, and the figures 1, 2, 3, 4 are written down on a piece of paper. The method of play is to stake the sum of the extreme figures, and if a win is scored, these two figures are erased; while if a loss is incurred the amount of the stake is written down at the end of the row of figures, and the next stake is the sum of the new extremes. When all the figures have been erased the coup is made, and the player either begins a fresh game or retires from the table. Here is an example: 1, 2, 3, 4: first stake 5, which is lost. The row now reads 1, 2, 3, 4, 5; and the next stake (6) is won, the row reading 1, 2, 3, 4, 5; the next stake (2+4) is lost, when we have 1, 2, 3, 4, 5, 6. The next stake is 8, which is won, and we read 1, 2, 3, 4, 5, 6; the next stake being 7, which is won, the 4 and 3 are erased, when it will be found that the net profit is 10 units.

Example of a bad run at a "Labouchere" system. The "grand coup" is 10; so the starting figures are 1, 2, 3, 4. The player is supposed to stake on Red throughout. The dot shows which colour wins.

The Figures. The Stake. R. B. Net + or –
1 01 + 4 005 • +5
2 02 + 3 005 ±0
3 02 + 5 007 –7
4 02 + 7 009 • +2
5 03 + 5 008 –6
7 03 + 8 011 • +5
8 00 + 5 005 ±0
5 05 + 5 010 –10
10 05 + 10 015 –25
15 05 + 15 020 –45
20 05 + 20 025 –70
25 05 + 25 030 • –40
25 05 + 20 025 • –15
35 10 + 15 025 –40
10 + 25 035 –75
10 + 35 045 • –30
40 15 + 25 040 –70
55 15 + 40 055 –125
70 15 + 55 070 –195
15 + 70 085 • –110
80 25 + 55 080 –190
105 25 + 80 105 –295
25 + 105 130 • –165
120 40 + 80 120 –285
160 40 + 120 160 –445
200 40 + 160 200 –645
40 + 200 240 • –405
215 55 + 160 215 –620
270 55 + 215 270 –890

Showing 29 coups, of which the player wins 9, with a net loss of 890 units. The next stake would have to be 55 + 270 (325), i.e. if the game had been played with a one louis unit, a heavier stake than is allowed at Roulette.

Systems are very amusing and profitable to play, provided nothing abnormal occurs. But something abnormal will occur sooner or later, and the amounts staked and lost become colossal, and finally the maximum is reached: no higher wager can be made, so the system fails. The flaw in all systems is that the losses on an unfavourable run are out of all proportion to the gains on a favourable one. A "Labouchere" runs into hundreds in no time, and is in fact one of the most treacherous systems to play for this reason. Let the reader dissect the play of a Labouchere on such a run as that on p. 460, which is a far from uncommon one.

This tableau, in which the player only wins 9 out of 29 coups—or, say, one in three—may be said to be far out of proportion, as the player is "entitled" to win as many coups as he loses (leaving zero out of the question). Let it be noted at this point that zero does not affect a system played on the even chances in any degree whatsoever. Any system worthy of the name can withstand zero, even two or three zeros. It is the Bank's limit, and the limit alone, that proves the downfall of all systems. To resume. Of course a player "ought" to win two coups out of four, and so he will as a rule, and systems are devised so that a player may be a winner, even if he loses three and four times as many coups as he wins. A glance at those figures not yet erased in the example quoted will show that had the punter not been debarred from staking, owing to the Bank's limit, with three successive wins he would have got all his money back and been ten points to the good on the whole transaction, and still have only won twelve times against the Bank's twenty. What no system, played with a Martingale, has yet been able to accomplish, is to prevent the stakes becoming colossal when the series of losses turn up in some particular sequence or disposition.

The best method to keep the stakes within reasonable limits, and to guard against arriving at the Bank's maximum on an adverse run, is to employ a varying unit. Thus after a net loss of so many single units, operations are re-started with a double unit; if an equal number of double units are lost, the play is re-started with a triple unit, and so on; the same unit being employed until all previous losses have been retrieved, and a gain of one "single" unit made.

A "Montant et demontant" system can be played very easily in this manner, by increasing the unit employed after each complete loss of ten units—e.g. after a loss of 10 single units, the system is started afresh with a double unit; when 10 double units have been lost, or a net loss of 30, the system is started afresh with a 3 unit stake, and so on.

This system may be varied by changing the unit after successive losses of 10, 20, 30, 40, &c., and by staking sufficient to show a net win of the amount of the unit employed. Thus when playing with a double unit, to try and win 2; or if playing with a unit of 5, to try and win 5 units net.

Every system has its Waterloo—it will succeed for days, possibly weeks, and small gains be made; but finally the occasion must and will arrive when all previous profits and the system player's capital will be swamped. At the end of this article will be found a scheme devised by the writer whereby the punter puts himself into the position of the Banker as nearly as possible, and consequently is enabled to win such vast stakes as are lost by a system player in the ordinary course, when that particular sequence of events occur which demolishes his system.

Here is an example of a "Montant et demontant" played in the usual method, and played with an increasing unit after each net loss of 10 units. The player is supposed to stake on the Red throughout; and the dot indicates which colour wins.

A varying Unit
R. B. Net
+ or –
R. B. Net
+ or –
01 –1 01 –1
02 –3 02 –3
03 –6 03 –6
04 –10 04 –10 Having lost 10 single units,
 the system is re-started
 with a double unit.
05 –15 02 –12
06 –21 04 –16
07 • –14 06 • –10
08 –22 08 –18
09 • –13 10 • –8
10 –23 09 –17 As the object is to be +1,
 9 is a sufficiently high
11 –34 11 –28
12 –46 02 –30 As not more than 30 may
 be lost while employing
 a double unit, 2 is the
 highest stake allowed.
13 –59 03 –33
14 • –45 06 • –27
15 • –30 09 • –18
16 • –14 12 • –6
15 –29 07 –13 As explained before.
16 • –13 10 • –3
14 • +1 04 • +1 As explained before.

Had the player lost 60 units, he would have re-started the system and played 4, 8, 12, &c.; and if this play showed a net loss of 100 units, 5, 10, 15, &c., would have been staked, and continued with until either the net loss was 150, or the net gain 1 unit, in which case the player would begin all over again with a single unit.

Another style of play is to bet on the prospect of the colour, or even chances, running in a particular way. Some people play for an intermittence of colour, consequently always stake on the opposite colour to that which turned up last. Others play for the run, and so always stake on the colour that last appeared. A very popular wager is to stake on the "Avant dernièr," or on the colour that turned up the last time but one. By this means there is only one combination of events by which the player loses, and this is if the colours go two of one kind, followed by two of the other; but the weak point about it is that the player may miss his first stake and his last one, although the series goes in his favour. Yet another common method of staking is to play "the card"—that is, to play in expectation of previous events repeating themselves. Thus if the previous throws have given three Blacks, followed by three Reds, the expectation is if three Blacks immediately occur, that three Reds will also occur.[110] Such theories, of course, have absolutely no scientific basis, and, in the opinion of the writer, are only vexatious and a cause of trouble to the player, who should invariably stake on the chance that is most convenient to where he is sitting. He has an equal chance of winning, and by this means will save himself the trouble of reaching across the table, both to place his stake and to retrieve his winnings.

There may be, however, some reason in playing for a run on one colour or chance, but not staking until after this colour or chance has appeared. By this means the player, if he plays flat stakes, is square on all runs of two, wins one on all runs of three, two on all runs of four, and so on. He loses one unit on every intermittence, but against this he loses nothing at all on all runs of the opposite colour or chance.

Had this method of staking been followed in the example given on p. 460, it will be seen that the player would have won 2 units on Red and 4 units on Black, and the highest stake necessary on any coup would have been 3 units; and had it been adopted in the example given on p. 457, only 70 units would have been lost on the Red side, and the highest stake risked 16; while on the Black, 41 units would have been won, with 9 as the highest stake.

It is advisable, when playing a system, to play on both sides of the table at once. The calculations for both Red and Black are kept, and the differences staked on the Red or Black as the case may be. The writer has actually seen a player stake the full requisite amount demanded by his system on both Red and Black at the same time. This of course gives the same net result as staking the difference on one colour, provided zero does not turn up. If it does, however, the player loses one-half of two large stakes in the one case, instead of only one-half of a small stake in the other case.

The advantage of playing a system on both sides of the table at the same time is that double as much can be won with the same capital that is required for playing on one side only. Indeed, slightly less capital is required, for obviously the player must be winning something on one side to go against his loss on the other. The objection, of course, to this dual system of play is, that there is a double chance of striking an adverse run.

While on the subject of where to stake one's money, the reader, if a novice at Monte Carlo, is recommended to hand the amount of his wager to one of the croupiers to place on the table for him. This will ensure both the money being placed exactly as the punter desires, and the receipt of any winnings, without disputes on the part of other players. Unless one's French accent is above reproach, it is advisable to talk English to the croupiers. The writer, wishing to stake on Nos. 3, 12, and 15 on one occasion, handed the chef-de-partie three 5-franc pieces, saying, "Sur le 3, 12, 15, s'il vous plaît." After a short conversation on the subject the chef said in perfect English, "If monsieur will please speak English, I will see that his money is correctly staked."

109 ^  See p. 469, footnote.
110 ^  This is a more common method of play at "Trente et Quarante" (see p. 468).