Of all the various wagering schemes that have been devised, only four are effective in minimizing losses: the consistent-wager system, the Martingale system, Oscar’s Grind, and Labouchere.
Consistent Wager System
This is the most widely-used money-management system: the player wagers a fixed amount on every hand dealt, regardless of the outcome of previous hands. By so doing, the player will, in the long run, lose no more that the house advantage against him—which is, if he practices perfect basic strategy—less than one percent.
In the short run, a single 90-hand session (45 hands per hour for two hours), the player is statistically likely to lose one more hand than he wins and end up “down” a single unit for the entire session. Granted, because statistics don’t bear out in the short run, the player will more often find the player “up” or “down” a modest amount depending on the order in which the cards happen to come out of the shoe. In the long run, these small wins and losses will balance out. Over the course of thousands of hands, or tens of thousands, the statistical probability of losing less than one percent of all hands played bears itself out.
Another advantage of the constant wager scheme is that it does not require a large bankroll. Because the amount only increases when the player elects to split or double down (which, statistically, is less than 4% of all hands in all situations), a player can buy in with 20 betting units (20 times the amount of his consistent wager) and expect to last the entire session. It’s worth mentioning that statistically improbable “losing streaks” do occur, which is why lasting the entire session can be expected, but is not certain.
Finally, as to the argument that the consistent wagering scheme is not a “system” at all: a player either wages systematically (according to a defined method) or at random (completely disorganized and chaotic). Though the amount of the wager is not varied, as in other systems, it is still planned and executed according to a strategy, a method, a system.
The Martingale system was developed in eighteenth-century France as a method for making money at red/black, even/odd, or high/low wagers at roulette, which makes it one of the oldest systems as well as the most effective. All other successful schemes are derivative of Martingale, though these derived schemes are generally not as effective.
The Martingale system is also very simple—the easiest system to learn, aside of the constant wagering scheme: the player begins at a single betting unit, then doubles the amount after each loss, returning to the original betting unit when a hand is won. If the player loses one hand, he wagers two units on the next—if he wins, he recoups the previous loss and stands one unit ahead. If he loses two hands in a row, his win on the third gains four units, covering his initial loss of one, his second loss of two, and leaving him one unit ahead. This continues, thus:
It is, however, effective—so much so that the rules of the game had to be changed to defeat it. Table limits were imposed to defeat players who “Martingaled” huge sums of money. With a table limit of 1,000 times the table minimum (which is typical), a player using the Martingale system will not be able to recoup his losses after the tenth loss, at which point he would be required to wager 1,028 units.
This cannot be said to make the system invalid. Not only could the player upgrade to a high-limit table if a streak of ten losses occurred, there is less than a 0.01% chance of such a streak occurring. These odds translate to once per thousand hands played, but are based on the statistics of independent events, so it would only be valid in games of blackjack where the cards are shuffled after every hand and cards that have been played do not bias the remaining hands by their absence.
Still, there are few players with the bankroll or the fortitude to faithfully follow the Martingale as losses continue to mount. This is why various systems were derived from Martingale, in which the increases in the wager, or the frequency with which increases are made, are decreased. Two of these derivative systems (Oscar’s Grind and Labouchere) are discussed hereafter.
A “Martingale-four” system instructed players to double up to twice (for a wager of four units) before returning to the original wager, and a “half-Martingale” system suggested that the bet should be increased by 150% rather than the full 200%. Since losses are not fully recaptured, these systems are not as effective as the original.
Others have attempted to improve upon Martingale by instructing to increase their wagers by more than double after each loss. The “Grand Martingale” system indicates to double, then add one more – to bet 1, then 3, then 7, then 15, then 31, etc. The result is, indeed, an increased profit because the loss recaptures more that previous wagers—but since the increase happens more rapidly, the player is likely to exceed the table limit much sooner, before the bias of the deck can turn in his favor.
Oscar’s Grind is based on playing hands as a series, with the goal of coming out of each series with a net win of at least one betting unit. It’s somewhat more conservative than Martingale because the increase in wagers is not as dramatic and does not occur as often—and like Martingale, the player can come out ahead if he has the tenacity and bankroll to play each series to its ultimately successful conclusion.
The player begins with a single unit—if that hand is won, the player has turned a one-unit profit, and the series ends. If the player loses a hand, the wager remains the same until another hand is won, at which point it’s increased by one unit. This continues until the player winds enough hands to recoup all previous losses, and come out one unit ahead, at which point the next hand is considered the beginning of a new series.
Here is an example of a series that persists for a dozen hands:
There are, however, two disadvantages to Oscar’s Grind. First, it is possible for a player to become “locked” into a very long grind. Whereas Martingale provides an instant recovery at the first win, this system may require a loser to win a number of hands before recovering all previous losses—and not to stop playing until the recovery has been made. Second, keeping track of the net balance over a long series of hands requires considerable concentration. The wagering system may become a distraction from playing basic strategy, and will almost certainly conflict with the ongoing math the player must concentrate upon to implement advanced strategies.
The Labouchere system instructs the player to adjust their wager based on the outcome of the previous hand, increasing after losses and decreasing after wins, but by a rather more complicated equation.
A sequence of numbers is chosen (1, 2, 3, 4, 5, 6) and the wager is determined by the sum of the first and last (in this case, 1+6 = 7). If the hand is won, the first and last numbers are removed (2,3,4,5) and the next wager is again the sum of the first and last (2+5 = 7). If the hand is lost, the total wager lost is added to the end of the series (from 2,3,4,5 to 2,3,4,5,7—so the next wager is 9—2+7). When all numbers are exhausted, the series has ended.
The net result is a slow but constant increase in the player’s wagers in a series of hands that, when the series is played to its conclusion, will ultimate leave the player ahead:
One final word of caution: if you plan to utilize a money-management scheme, it is crucial to have the fortitude to stick with it. If you blanch at having to wager a large amount in order to recover your losses, or become discouraged by the feeling of being “locked” into a long grind, you may be tempted to join the herd of players who, having failed to stick to a system, pronounce the system itself a failure.