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.