| Updated: Various strategies and systems in gambling claim to improve the odds of winning. However, this is rarely the case with casino games, as games such as roulette and craps have a house edge that gives the casino an advantage over its players. Still, gamblers have used certain progressive betting systems for decades in an attempt to increase potential winnings and limit losses.
Progressive systems consist of fixed rules for adjusting the size of a bet based on the outcome of the previous round. Some systems instruct players to increase their bets after a win, while others recommend raising the bet after a loss. Some betting progressions, as they are also known, require players to double their bets after each round. This approach can be very risky, but these betting systems remain popular among gamblers. Certain progressive betting systems are also used in craps, and this article outlines their basic rules and concepts.
Negative Progressive Systems
There are two main types of progressive betting systems – negative and positive. Negative progressions are especially popular because they promise a way to recoup losses and potentially generate sizable profits overall. In essence, the idea is to increase the size of the bet after each lost gaming round, while after a win, players are advised to reduce the amount they wager. In theory, after a few losses the bet becomes so large that a single win would be enough to recover all previous losses and produce a profit equal to or greater than the original stake.
The Martingale
Labouchere System D’Alembert System The Fibonacci SequenceThe Martingale
The oldest and most famous betting system is the Martingale. Used since the 18th century in various gambling games, it is suitable whenever even-money bets are offered, such as red or black in roulette and Pass or Don’t Pass in craps. The system is very simple, which is why it has become so popular among gamblers. It has only two rules:
- Players double the bet after they lose.
- After they win, they place their original bet.
The Martingale is also easy to apply in practice. Players start by placing 1-unit wagers on even-money bets, such as Pass/Don’t Pass or Come/Don’t Come. They continue making the same type of wager throughout the session and double their stake after each loss. Whenever they win, they restart the progression and bet a single unit.
The system is very risky because it can lead to wagering large amounts of money after only a few losses. For example, if we start with a $10 Pass Line bet and keep losing, the stakes quickly rise to $20, $40, $80, and $160. The total amount wagered after five consecutive losses is $310. If the next $320 bet wins, the net profit is exactly one unit, or $10 in this case. Provided the progression ends with a win, the profit is always one unit.
The progression can end prematurely if the player has insufficient funds, which is the primary risk of the Martingale. Using it requires a sizable bankroll and the lowest starting wager possible.
Labouchere System
Another popular negative progressive system is the Labouchere system, invented by the English politician, author, and roulette player Henry Labouchere. Also known as the Cancellation System or the Split Martingale, this progression is slightly more complicated. Like the Martingale, it increases bets after each loss, but it aims to recover losses over several wagers rather than with a single win.
The progression begins with a sequence of numbers whose sum represents the target profit. For instance, if our target profit is $10, we might use the sequence 1-1-2-3-2-1. We place the first bet by adding the first and last numbers in the sequence, so the initial wager is $2 (1+1). Once again, the Labouchere system applies to the Pass/Don’t Pass or the Come/Don’t Come wagers.
After a win, the two numbers at opposite ends of the sequence are removed, and the next bet would be $3 (1+2). If the bet loses, however, we add its amount to the right end of the sequence, so 1-2-3-2 becomes 1-2-3-2-3. Following the same logic, the next wager would be $4 (1+3). The progression ends when all the numbers have been removed. If only one number remains, that number is used for the next bet.
- The progression uses a sequence of numbers, and the first bet is the sum of the first and last numbers.
- After a win, the first and last numbers are removed from the sequence.
- After a loss, the amount of the losing bet is added to the end of the sequence.
If the sequence is completed successfully, the profit equals the sum of the original numbers. Using the example above, the target profit is $10. Although the system may seem complicated, it is relatively easy to apply because players can write down the numbers they have chosen. It is also flexible, as players can select values based on their bankroll. A sequence with a target profit of $10, for instance, could be 1-1-3-3-1-1, 1-1-1-1-1-1-1-1-1-1, or 5-5.
D’Alembert System
Named after the French mathematician and philosopher Jean le Rond d’Alembert, this system uses a negative progression in which bets are raised after a loss and decreased after a win. It is based on the popular gambler’s fallacy that a series of one outcome should be followed by a similar number of opposite outcomes. Applied to craps, this means that after playing for a certain amount of time, such as four hours, players may expect roughly the same number of wins and losses.
The d’Alembert system is easy to use. Players start with a 1-unit wager on an even-money bet such as the Pass Line. If they lose, they increase the bet size by 1 unit; if they win, they reduce it by 1 unit. If the original bet is $10 and it loses, we increase it to $20. If this bet also loses, we wager $30. If we then win, we decrease the bet to $20.
- After a loss, the bet increases by 1 unit.
- After a win, the bet decreases by 1 unit.
This system is more conservative than the Martingale because the size of the stakes increases gradually. Although it may produce short-term profits, it cannot overcome the house edge. Even during a winning streak, the profits may not be as high as expected.
The Fibonacci Sequence
This system is one of the more unusual gambling systems. It uses the famous Fibonacci sequence, a series of numbers in which each entry is the sum of the two preceding numbers. The sequence starts with 0, which is not used for wagering, so the Fibonacci progression for craps includes the following numbers:
- 1-1-2-3-5-8-13-21-34-55-89-144, etc.
- After a loss, players bet units equal to the next number in the sequence.
- After a win, players move back two numbers in the sequence.
To apply the Fibonacci sequence, craps players should stick to an even-money bet and follow these basic rules. The idea is that wins following several losses will help recover the losses accumulated during the progression. Although straightforward in theory, this system has the same drawback as other negative progressions. If players lose multiple bets in a row, the stakes can rise rapidly and become unaffordable.
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Positive Progressive Systems
Positive progressive systems are the opposite of negative betting systems and are quite popular among gamblers. With these methods, casino players increase the size of their bets after they win a game round and reduce their wagers after a loss. The goal is to maximize profits during winning streaks while keeping losses to a minimum.
The Paroli System Reverse Labouchere System The 1-3-2-6 System Contra d’Alembert SystemThe Paroli System
The Paroli is a popular betting system for games such as roulette, baccarat, and craps. First described in 1910 by Victor Bethell, the system is believed to be much older. It is very simple to learn and apply in real-money games because it follows only a few basic rules:
- Players start the progression with a single betting unit.
- After a win, they double their current bet.
- After a loss, they stop the progression and start from the beginning.
- The progression ends after three consecutive wins.
To illustrate the Paroli system, let’s use $10 as our original betting unit and place it on an even-money bet such as the Pass Line. If the shooter rolls a 7 on the come-out roll, we win and double our stake to $20. If this bet wins, the next wager becomes $40. If the $40 wager also wins, the progression ends after three consecutive wins, and we restart the system with the original $10 bet. Every time we lose, we return to the initial bet and start over.
Many players prefer this system because the progression is relatively short and the stakes increase only a few times. However, it relies entirely on winning streaks to generate a profit and cannot automatically recover losses accumulated over time. The maximum profit from one completed Paroli sequence is seven betting units, while the maximum loss in one unsuccessful sequence is one unit.
Reverse Labouchere System
The essence of this method is evident in its name. As a positive progression, it is the opposite of the negative Labouchere system. Players begin by writing down a sequence of numbers that will serve as the basis for their bets. Using the sequence 1-1-2-3-2-1, how does this version differ from the original?
- Players add the first and last numbers in the sequence to determine the size of the first bet.
- After a win, they add their current bet to the right end of the progression.
- After a loss, they remove the first and last numbers from the sequence.
If we use the 1-1-2-3-2-1 sequence, our first bet will be $2 (1+1). After a win, we add the wager to the right end of the sequence, creating 1-1-2-3-2-1-2. The next bet is $3, and if it wins, the progression grows to 1-1-2-3-2-1-2-3. The following wager would then be $4. This system is flexible, and players can choose the numbers in the sequence. However, the larger the numbers are, the higher the stakes will be.
Players should also establish win limits because the progression can become very long during extended winning streaks. Another important point is that the Reverse Labouchere system does not guarantee profits, even in the short term. Its success in increasing winnings depends entirely on chance.
The 1-3-2-6 System
Another positive progression that is fairly popular among gamblers is the 1-3-2-6 system. Like other progressive betting systems, it can be applied to a wide variety of casino games that offer even-money bets, including craps. Those who use the 1-3-2-6 method should continue making the Pass Line, Don’t Pass, Come, or Don’t Come bets.
- The system follows the 1-3-2-6 sequence. It starts with 1 betting unit and ends after the fourth step.
- After a win, players adjust the bet size according to the sequence.
- After a loss, players stop the sequence and start over.
This system is simple to use. Let’s say our betting unit is $10 and we win several times in a row. Our first bet will be $10, followed by a $30 bet, then $20, and finally $60. The maximum profit from one sequence is 12 betting units, while the maximum loss is 2 units. This loss occurs if players lose on the second step of the sequence. Although this progression seems straightforward, it can still lead to substantial financial losses if players repeatedly lose on the second step.
Contra d’Alembert System
The Contra d’Alembert system, also known as the Reverse d’Alembert system, is another positive betting progression that can be used for even-money bets such as the Pass Line and Don’t Pass in craps. Like many progressive systems, this method can be associated with the false premise that previous outcomes affect the result of the next bet. In craps, as in any other game of chance, the outcome of the current round is independent of previous outcomes.
Even so, the Contra d’Alembert system is still used by some players who believe it helps them control their betting and maximize potential winnings. The method is easy to implement in real-money games and follows these rules:
- Players start the progression with a 1-unit bet.
- After a win, they increase the bet size by 1 unit.
- After a loss, they decrease the bet size by 1 unit.
Unlike systems that require complicated calculations or long sequences of numbers, the Contra d’Alembert system is very simple. However, it cannot guarantee consistent profits or change the house edge. The more players win, the more they wager, while their stakes decrease after losses.