the player plays black, black, black, red, and so on in an exactly opposite sense, increasing his stake till successful. As a matter of fact it is not very usual for any given number of coups to recur in exactly the same succession, and played with discretion this system occasionally yields fair results.
Another simple method is to stake red, black, alternately, doubling up till the winning colour is caught. This has the advantage of ensuring profit from a run, but a directly opposite series of alternate reds and blacks must, of course, prove ruinous in the extreme.
The martingale, which is merely going "double or quits," is the simplest of all systems. There are two martingales, the small and the great. In the small martingale the aim is to get back all previous losses in one coup, and to leave you a winner of one unit at the finish.
The progression is as follows: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. If you played this system at a roulette table with a unit of five francs, it takes eleven consecutive losses to defeat you, and one loss less at the trente-et-quarante table, where the minimum stake is 20 francs.
You may go on playing this martingale for weeks at a time without encountering an adverse run of sufficient magnitude to enable the bank to capture your stake. The only thing you have to fear is a run of 12 against you; you can only double up eleven times, and your last stake will be 5120 francs. Runs of 12, however, are rare.
The great martingale aims at getting back all the previous losses and winning one unit for every coup played. The progression is 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, and the player is defeated by ten consecutive losses at roulette, and nine at trente-et-quarante.
When playing the little martingale the player has to double his stake every time he loses, in order to recover his losses and be one unit to the good. Whereas, in the great martingale he not only doubles his stake but adds one unit to each coup, and only stands one chance in 1024 of losing at each coup, that is, of encountering an adverse run of ten.
A popular system is that known as the Labouchere system. Its main principle is to keep scratching out the top and bottom figures whenever you win, till no figures are left, and always to put down your loss when you lose, which, added to the topmost number, forms the next stake.
Before beginning to play write down on a card 1, 2, 3, in this order:—