There are various strategies and systems in gambling that are said to improve the odds of winning. This is hardly true when it comes to casino games, however, since games such as roulette or craps have a house edge that gives casinos the advantage over their patrons. Still, certain progressive betting systems have been used for decades by gamblers in order to increase the potential winnings and limit the expected losses.
Progressive systems consist of fixed rules about adjusting the size of the bet based on a previous outcome. According to some systems, players need to increase their bets after a win, while other progressive systems recommend increasing the bet after a lost round. Some betting progressions, as they are also known, double the size of the bet after each gaming round. This, of course, could be very risky, yet some betting systems are incredibly popular among gamblers. Certain progressive betting systems are also used in craps play, as well, and this article outlines their basic rules and concepts.
Negative Progressive Systems
There are two main types of progressive betting systems, namely negative and positive. The negative progressions are the most popular betting methods since they promise a way to return your losses and huge 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 of money they wager. In theory, after a few losses, the bet should be so high that only one win would be sufficient to recover the losses and bring a profit equal to or larger than the original stake.
The Martingale 
Labouchere System 
D’Alembert System 
The Fibonacci Sequence The 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 the red and black in roulette or the Pass and Don’t Pass bets 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 make 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 keep making the same bets throughout the entire game session and after each loss, they double their bets. Whenever they win, they start the progression from the beginning and bet a single unit.
The system is very dangerous, however, because it can result in betting huge amounts of money after just a few losses. If we start our progression with a $10 Pass Line bet, for example, and we keep losing, the bet would quickly rise to $20, $40, $80, $160 for a total bet of $310 after five losses in a row. If we win the next bet, our profit will be exactly one unit, $10 in this case. In fact, it does not matter how much we win or lose – at the end of the progression, the profit will always be 1 unit.
The progression cannot end, however, with insufficient funds, which is the real risk of the Martingale. In order to use it, players should have a sizable bankroll and start with the lowest wagers possible.
Labouchere System
Another rather 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 the bets after each loss but it returns the losses with several wagers, rather than with a single one.
The progression includes a sequence of numbers, which sum will be our target profit. For instance, our target is $10, so we make the following progression – 1-1-2-3-2-1. We start the system by adding the first and last numbers from the sequence and this is the first bet. In this case, it 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 should be removed and the next bet would be $3 (1+2). If the bet loses, however, we add its amount at the right end of the sequence and 1-2-3-2 would become 1-2-3-2-3. Following the same logic, next, we will bet $4 (1-3). The progression ends when there is a single number left in the sequence of numbers. Then, we use that number for our 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 each sequence, the result will be equal to the sum of all the numbers in it. However, this could be a profit or a loss. Using the example from above, the progression can either end with us winning $10 or losing exactly $10. Although this system seems complicated, it is actually very easy to apply in real-life games considering players write down the numbers they have chosen. Another great thing about this betting progression is that it is extremely flexible as players select the different bets sizes, based on 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 the opposite outcomes. If applied to a game of craps, this means that after playing for a certain amount of time – four hours, for example, players should have accumulated roughly the same number of wins and losses.
The d’Alembert system is very easy to use – players start by making 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 and 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 bet $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 since the size of the stakes here increases gradually. Although this method can help players make short-term profits, they will eventually lose money because of the house edge. Even if they are on a winning streak, their profits would not be as high as they expected.
The Fibonacci Sequence
This system is probably one of the strangest gambling systems ever created. It utilizes the famous Fibonacci sequence, a sequence of numbers used in mathematics – in it, the sum of the previous two numbers comes as the next entry. The sequence starts with a 0, which is not used when gambling, so for craps play, the Fibonacci progression 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 following number in the sequence.
- After a win, players move down two numbers in the sequence.
To apply the Fibonacci sequence, craps players should stick to one of the even-money bets and follow the basic rules. The idea is that even after they lose several bets, they will be able to return the losses when they eventually win. While theoretically solid, this system has the same problem as all other negative progressions – if players lose multiple bets in a row, the size of the stakes could rise really high and become practically unaffordable.
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Positive Progressive Systems
Positive progressive systems are the exact opposite of the negative betting systems and are also quite popular among gamblers. With them, casino players increase the size of their bets after they win a game round. Of course, after a loss, they reduce the bets. The idea behind this style of betting is to maximize one’s profits when players are on a winning streak. The other purpose of the positive progressions is to keep the losses to the minimum.
The Paroli System 
Reverse Labouchere System 
The 1-3-2-6 System 
Contra d’Alembert System The Paroli System
The Paroli is a highly popular betting system for various games, including 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 since it follows only several 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 describe the Paroli system more clearly, let’s take $10 as our original 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 bet to $20. If this bet wins, the next wager becomes $40 – when it wins, we double once again to $80. Here, the progression ends and even if this wager wins, we must start the system from the beginning. Of course, every time we lose, we return to the initial bet and start all over.
Many players prefer using this system because it is relatively safe and with it, the bets increase only a few times. At the same time, those who apply it are unlikely to suffer significant losses. However, the system relies solely on winning streaks to generate any profits, while it is not capable of returning any losses incurred over time. The maximum profit with the Paroli is exactly 7 betting units – when the progression ends, we can win up to 7 betting units and lose up to 1 unit.
Reverse Labouchere System
The essence of this method clearly shows in its name – a positive progression, it is basically the opposite of the negative Labouchere system. Players who decide to use it will start the progression by writing down a sequence of numbers that would be the base for their bets. If we take the Labouchere sequence from above, we have 1-1-2-3-2-1 but how is it different from the original system?
- Players add the first and the last number from the sequence to have 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 add the bet at the right end of the sequence to have 1-1-2-3-2-1-2. The next bet should be $3 and if it wins, the progression continues to grow – 1-1-2-3-2-1-2-3, while the next wager would be $4. This system is flexible and players are free to choose the numbers in the sequence. They should know, however, that the greater the numbers in the sequence, the higher their bets will be.
Players should also determine win limits since the progression could become incredibly long after several winning streaks. Another important thing about the Reverse Labouchere system is that it does not guarantee profits – not even in the short term. Its effectiveness in increasing one’s winnings depends solely on chance.
The 1-3-2-6 System
Another positive progression that is fairly popular among gamblers is the 1-3-2-6 system. Just like the rest of the progressive betting systems, it can be applied in a wide variety of casino games with even-money bets. This includes craps and those who want to use the 1-3-2-6 method should keep making the Pass Line, the Don’t Pass, the Come or the Don’t Come bets.
- The system uses the 1-3-2-6 sequence – it starts with 1 betting unit and ends after the fourth step.
- After a win, players continue to change the bet size according to the sequence.
- After a loss, players stop the sequence and start all over again.
This system is quite simple to use – let’s say our betting unit is $10 and win several times in a row. Our first bet will be $10, followed by $30 bet, then $20, and the last bet in the progression will be $60. The maximum profit from this system is 12 betting units and the maximum loss that could be generated is merely 2 betting units – this could happen if players lose after the second step of the sequence. While this betting progression seems quite safe and simple, it could lead to sizable financial losses if players keep losing after the second step of the sequence.
Contra d’Alembert System
The Contra d’Alembert System, also known as the Reverse d’Alembert System, is another positive betting progression that could be used for even-money bets such as the Pass Line and the Don’t Pass bet in craps. Just like the original negative system named after the French mathematician, this method is based on a false premise – that players are more likely to win after a losing bet. In craps, as in any other game based on chance, the outcome of the current round is independent of the past outcomes.
That being said, the Contra d’Alembert System is still used by some players who believe that it helps them control their betting and maximize their potential winnings. The method is quite easy to implement in real-money games. It follows these several 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, which include complicated calculations or long sequences of numbers, the Contra d’Alembert System is very simple and promises small, yet consistent profits over time. The more players win, the more they wager. Meanwhile, they can keep the expected losses to the minimum.