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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 a.s.sumed 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]
a.s.suming 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 a.s.suming 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 _pet.i.t coup_ time after time with perfect equanimity, and only wishes he had had the other qualifications as well.
Referring for one moment to the a.s.sumed 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 a.s.sured 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, _a.s.sume_ 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-fas.h.i.+oned 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] p.r.o.nounced _Back[)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 t.i.tle 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 Bezique.
[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_ (Cavaille). t.i.t. "Les Pet.i.ts 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), t.i.t. "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, Ma.s.sachusetts, 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 ent.i.tling the holder to the deal.