| Updated: September 25, 2025There are various strategies and systems in gambling that claim to improve the odds of winning. However, this is rarely the case for casino games, as games such as roulette and craps have a house edge that gives the casino an advantage over its patrons. Still, gamblers have used certain progressive betting systems for decades to increase potential winnings and limit expected losses.
Progressive systems consist of fixed rules for adjusting the size of a bet based on the outcome of the previous round. According to some systems, players should 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 bet after each round. This approach can be very risky, yet these betting systems remain incredibly 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. Having been used since the 18th century in various gambling games, it works best when even-money bets are offered, such as red/black in roulette or Pass and Don’t Pass in craps. The system is very simple, which is why it has become so popular with 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 very easy to apply in practice – players start by placing 1-unit bets on fifty-fifty options (almost 50/50) such as the Pass/Don’t Pass or the Come/Don’t Come bets. They continue making the same wager throughout the entire gaming session, and after each loss they double their stake. Whenever they win, they restart the progression and bet a single unit.
The system is very dangerous, however, because it can lead to wagering huge amounts of money after just a few losses. If we start with a $10 Pass Line bet and keep losing, the stakes would quickly rise to $20, $40, $80, and $160 – for a total outlay of $310 after five consecutive losses. Should we win the next bet, our net profit would be exactly one unit, $10 in this case. In fact, no matter how many wins or losses occur, the progression always produces a profit of just one unit.
However, the progression can be cut short by insufficient funds, which is the real risk of the Martingale. To use it, players should have a sizable bankroll and start with the lowest wagers 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 a bit more complicated. Just 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 write the sequence 1-1-2-3-2-1. We place our 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 the 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 only one number remains in the sequence. We then use that number for the final bet.
- The progression includes a sequence of numbers and starts with the first and last numbers as the first bet.
- After a win, the first and the last numbers are removed from the sequence.
- After a loss, the sum of the first and last numbers is added at the end of the sequence.
At the end of the sequence, the result will be equal to the sum of all the numbers in it. This can be either a profit or a loss. Using the example above, the progression can end with us winning $10 or losing exactly $10. Although the system may seem complicated, it is easy to apply in real-life games because players simply write down the numbers they have chosen. Another advantage is its flexibility, as players can tailor bet sizes to their bankroll. The sequence for 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 certain number of outcomes should be followed by the same number of opposite outcomes. Applied to craps, this means that after playing for, say, four hours, players expect roughly the same number of wins and losses.
The d’Alembert system is very 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 the bet by 1 unit. If the original bet is $10 and it loses, we increase it to $20. If this bet loses again, we wager $30. If we win this time, we decrease it to $20.
- After a loss, the bet increases by 1 unit.
- After a win, the bet decreases by 1 unit.
As we can see, this system is more conservative and safer than the Martingale because the size of the stakes increases gradually. Although this method can help players earn short-term profits, they will eventually lose money because of the house edge. Even on a winning streak, the profits may not be as high as expected.
The Fibonacci Sequence
This system is probably one of the most unusual gambling strategies ever devised. It relies on the famous Fibonacci sequence, a series of numbers in which each entry is the sum of the two preceding numbers. Because the sequence begins with 0, which is not used in wagering, the practical Fibonacci progression for craps is:
- 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 simple rules. The idea is that after several losses, a subsequent win will recover the losses when it eventually occurs. While theoretically sound, this system shares the main drawback of all negative progressions – if players lose multiple bets in a row, the stakes can escalate rapidly and become practically 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 highly popular betting system for games such as roulette, baccarat, and craps. Although 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 wins.
To illustrate the Paroli system, let’s take $10 as our betting unit and place it on an even-money bet such as the Pass Line. If the shooter throws a 7, we instantly win and double our stake to $20. If this bet wins, the next wager becomes $40; when it wins, we double once again to $80. At this point the progression ends, and even if the $80 wager wins, we must restart the system. Of course, every time we lose, we return to the initial bet and start over.
Many players prefer this system because it is relatively safe; the stakes increase only a few times, making significant losses unlikely. However, the system relies entirely on winning streaks to generate profit and cannot recoup losses accumulated over time. The maximum profit with Paroli is exactly seven betting units, while the maximum loss in a single sequence is just 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 the last number 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 the last number 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 append 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, with the following wager being $4. The system is flexible, allowing players to choose any numbers they like; the larger the numbers, however, the higher the stakes will be.
Players should also establish win limits, as the progression can become incredibly 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 boosting 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 most progressive betting strategies, 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 keep 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 quite 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 in one sequence is 12 betting units, while the maximum loss is merely 2 units – this occurs if players lose after the second step of the sequence. Although this progression seems safe and straightforward, it can still lead to substantial financial losses if players consistently lose after the second step.
Contra d’Alembert System
The Contra d’Alembert System, also known as the Reverse d’Alembert, 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 the original negative system named after the French mathematician, this method rests on a false premise – that players are more likely to win after a losing bet. In craps, as in any game of chance, the outcome of the current round is independent of previous results.
Even so, the Contra d’Alembert System is still favored 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 simple 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 some systems that require complicated calculations or long sequences of numbers, the Contra d’Alembert System is very simple and aims for small yet consistent profits over time. The more players win, the more they wager, while expected losses remain limited.