Hoyle's Games Modernized Part 61

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. {457} 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= 1 + 4 5 +5 =2= 2 + 3 5 0 =3= 2 + 5 7 -7 =4= 2 + 7 9 +2 =5= 3 + 5 8 -6 =7= 3 + 8 11 +5 =8= 5 5 0 =5= 5 + 5 10 -10 =10= 5 + 10 15 -25 =15= 5 + 15 20 -45 =20= 5 + 20 25 -70 =25= 5 + 25 30 -40 =25= 5 + 20 25 -15 =35= 10 + 15 25 -40 10 + 25 35 -75 10 + 35 45 -30 =40= 15 + 25 40 -70 55 15 + 40 55 -125 =70= 15 + 55 70 -195 15 + 70 85 -110 80 25 + 55 80 -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 {458} 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 "ent.i.tled" 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 {459} 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 {460} 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.

+-------------------+-------------------+------------------------------+ Ordinary A varying Unit Method. employed. Remarks. +-------------------+-------------------+ R. B. Net R. B. Net +or- +or- +------+-----+------+------+-----+------+------------------------------+ 1 -1 1 -1 2 -3 2 -3 3 -6 3 -6 4 -10 4 -10 Having lost 10 single units, +------+-----+------+ the system is re-started 5 -15 2 -12 with a double unit. 6 -21 4 -16 7 -14 6 -10 8 -22 8 -18 9 -13 10 -8 10 -23 9 -17 As the object is to be +1, 11 -34 11 -28 9 is a sufficiently high stake. 12 -46 2 -30 As not more than 30 may +------+-----+------+ be lost while employing 13 -59 3 -33 a double unit, 2 is the 14 -45 6 -27 highest stake allowed. 15 -30 9 -18 16 -14 12 -6 15 -29 7 -13 As explained before. 16 -13 10 -3 14 +1 4 +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., {461} 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 dernier_," 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.

{462}

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 {463} 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 plait._" 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."

{464}

TRENTE ET QUARANTE.

BY CAPTAIN BROWNING.

TRENTE ET QUARANTE is played with six packs of cards on a table marked out as in the ill.u.s.tration (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.

[Ill.u.s.tration: FIG. 3.]

{465} 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 ill.u.s.tration (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 {466} 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 pa.s.sent_,"

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 ident.i.ties of the points, by the word "_apres_." Thus suppose the Black row counts up to 38, and the Red row to the same figure, the _tailleur_ announces "_Huit, huit apres_." If it happens to be a _Refait_, he says, "_Un, un apres_," 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 {467} 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 a.s.sume 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 {468} 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_ {469} sends for some more money, which is "_Ajouter a 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 a.s.sumptions:--

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 _a.s.sumed_, 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 {470} (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 2 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.)