Part 29

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 {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 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 {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 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 {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 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 {471} 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 {472} 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= 1 + 4 5 · -5 =2= 2 + 3 5 · 0 =3= 2 + 5 7 · +7 =4= 2 + 7 9 · +16 =5= 2 + 9 11 · +27 =7= 2 + 11 13 · +14 =9= 3 + 9 12 · +2 =11= 5 + 7 12 · +14 =12= 5 + 12 17 · +31 =17= 5 + 17 22 · +53 =22= 5 + 22 27 · +80 =27= 5 + 27 32 · +48 7 + 22 29 · +19 =29= 12 + 17 29 · +48 =41= 12 + 29 41 · +89 12 + 41 53 · +36 =46= 17 + 29 46 · +82 17 + 46 63 · +19 =29= 29 29 · +48 58 29 + 29 58 · +106 =87= 29 + 58 87 · +193 29 + 87 116 · +77 =87= 29 + 58 87 · +164 29 + 87 116 · +48 58 58 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. {473}

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 {474} 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. {475}

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.

Printed by BALLANTYNE, HANSON & CO. Edinburgh & London

* * * * *

NOTES

[1] This is the old-fashioned rule, but at the present day the Whist rule of "lowest card deals" is frequently followed.

[2] See note on last page.

[3] For the accepted Laws of All-Fours, see _The Book of Card and Table Games_ (Routledge).

[4] Pronounced _Báck[)a]rah_.

[5] The number is not absolute, sometimes four packs, sometimes two only, being used; but three is the more usual number.

[6] For the Laws of _Baccarat Banque_, and some suggestions for play, see _The Book of Card and Table Games_.

[7] Some players do not score _brisques_ till the close of the hand. The better rule, however, it to score them when the trick is won.

[8] In some circles, when the Whist tricks are reached, the ten reverts to its Whist rank, _i.e._ below the knave, but the practice is not recommended.

[9] _Carte blanche_ is scored at the outset of the game, and before the player has drawn a card. He must prove his title by exhibiting his nine cards, one after another (as rapidly as he pleases), face upwards on the table. Should the first card he draws not be an honour, he may show the card, and again score _carte blanche_, and so on, as often as this may happen; but _carte blanche_ cannot be scored after the player has once held a court card.

[10] The first marriage scored is necessarily in trumps.

[11] It will be observed that this rule is directly contrary to that prevailing at ordinary Bézique.

[12] Roughly, the value of all the brisques in the four packs. There are actually 32, which at ten each would be 320; but as the odd 20 are not reckoned, this reduces the value to 300.

[13] As a matter of fact, this arrangement is no guarantee whatever against pre-arranged fraud. For the methods employed by card-sharpers at this game, see _Les Filouteries du Jeu_ (Cavaillé). Tit. "Les Petits Paquets."

[14] Court cards, though they all count as of the same value--_i.e._ "ten"--retain their distinctive rank for pairing purposes. Thus a knave can only be paired with a knave, and so on.

[15] A single fifteen is spoken of as fifteen two, two fifteens as fifteen four, three as fifteen six, and so on. Four (fifteen eight) is the largest number of fifteens that can be made with four cards.

[16] If the knave and start be of different suits, the score is twenty-eight. With four fives in the crib, and the knave turned up, the value of the show will be twenty-eight only, but the dealer will already have scored "two for his heels," so that the total value is thirty.

[17] The score is made up as follows. Each of the sixes combines with each nine to make a fifteen, giving fifteen four. Again, each of the threes combines with the two sixes, bringing the score to fifteen ten. The pair and pair-royal make it eighteen.

[18] If the three tenth cards make neither pair nor sequence, the score will be fourteen only.

[19] In the case supposed, it would be very unwise for A to pair the eight, as, in the event of B's holding a second eight, he would make a "pair-royal" and "go" simultaneously.

[20] There is no authoritative code of Cribbage Laws, and there is considerable divergence of opinion on sundry minor points. For the rules generally accepted, the reader may be referred to the _Book of Card and Table Games_ (Routledge), tit. "Cribbage."

[21] De la Rue & Co.

[22] The elder hand may "propose," _i.e._ ask for cards, as often as he pleases. If the dealer is not content with his own hand, he will give cards, but after the first proposal, it is entirely at his own option whether or not to do so.

[23] For some further rules, defining the position and obligations of bystanders betting on the game, see the work of "Cavendish" referred to at p. 53.

[24] A still higher trump is sometimes by agreement introduced in the shape of a blank card, backed like the rest of the pack which in this case consists of thirty-three cards. This is known as the "Joker," or "Best Bower," and takes precedence even of Right Bower. If the "Joker" chance to be turned up, the card next in order decides the trump suit.

[25] Under the more modern practice the player having the later call _can_ play alone in place of his partner. Only a very strong hand, however, would justify his doing so.

[26] There is no English Code of Laws for Euchre. The accepted American Code was compiled in 1888 for the Somerset Club, Boston, Massachusetts, by Messrs. H. C. Leeds and James Dwight. It will be found reprinted at length, by their permission, in the _Book of Card and Table Games_.

[27] This is usually done by dealing a preliminary round, face upwards, the first knave turned up entitling the holder to the deal.

[28] As, for instance, where the player holds the seven and nine of trumps, the eight having been turned up; the seven and nine are then of equal value.

[29] Sometimes the preference is given to the elder hand, irrespective of the value of the cards.

[30] The words between brackets apply of course to three-card loo. Sometimes the dealer is allowed, after dealing one card to each player, to deal three together for a miss, but the practice is irregular.

At five-card Loo the _Écarté_ method of dealing (first by threes, and then by twos, or _vice versâ_) is sometimes adopted.

[31] For an instructive series of illustrative hands at Napoleon, see the _Book of Card and Table Games_.

[32] A having made seven out of twelve.

[33] See in particular the excellent treatise on the game by "Cavendish," published by Messrs. De La Rue & Co.

[34] For the authorised Laws of the Game, in its modern form, see _The Book of Card and Table Games_, or the treatise of "Cavendish" before mentioned.

[35] As the game is sometimes played, the dealer, and not the Age, puts up the _ante_, but the contrary is the more usual practice.

[36] This being a compulsory stake on an unknown hand, it is prudent to make it as small as possible.

[37] The Age, as a rule, goes in, even with poor cards; if he passes, he is bound to lose the half stake already put up, and it is, therefore, generally worth his while to risk the other half.

[38] Should B have already thrown up his cards, the privilege does _not_ pass to C. There is a maxim on this point, "The Age never passes."

[39] Some players on a second round only allow the jack-pot to be opened by a pair of queens, or better; on a third, only by a pair of kings, or better; and on a fourth, only by a pair of aces, or better; but the practice is not recommended.

No player, even though holding the needful cards, is bound to open the jack-pot unless he pleases.

[40] Strictly speaking, each dealer in rotation should himself dress the board, but it will be found more convenient to depute some one player to do so throughout the game.

[41] By some players the dealer is allowed the privilege of looking at the extra cards (sometimes, but incorrectly, themselves spoken of as "the stops"), and to act as a kind of referee as to whether a given card is a stop or otherwise, but the practice is not recommended.

[42] The Misère is now introduced into Napoleon. See p. 96.

[43] For more minute information, and for a number of illustrative hands, see _The Book of Card and Table Games_.

[44] The right to deal is usually decided by a preliminary deal of faced cards, the first ace, or first knave, as may be agreed, having the preference.

In some circles, after the cards are cut, the dealer is allowed to look at the bottom card, and if such card prove to be an ace or tenth card, he also looks at the top card. If the two form a "natural," he is entitled to receive double the _minimum_ stake all round.

This privilege is known as the _brûlet_, from the fact that it is dependent on the nature of the bottom card, which is always, in the French phrase, _brûlé_ (literally, "burnt") _i.e._ thrown aside when reached in the course of the deal, and not dealt to any player.

The _brûlet_ has never been recognised as an essential part of the game, and is now generally abandoned.

[45] Some players risk the maximum stake on a seven, but we question the expediency of doing so.

[46] This amount is the same as is paid for an ordinary Vingt-Un, _i.e._ one made with more than two cards. Sometimes, by agreement, a "natural" receives double the amount of an ordinary.