Progressive Roulette Systems

Martingale - The King of Betting Progressions

The Martingale is easily the most popular strategy among gamblers and is used in games such as roulette, blackjack, craps, and baccarat. It is not clear who devised the system, although some sources suggest it was named after 17th-century casino owner Henry Martindale. The name’s pronunciation reportedly changed over time.

This is a negative progressive system in which you double your stake after each loss and return to your base unit after a win. It can be applied to all types of roulette bets, but it is mostly used for even-money propositions such as red/black, even/odd, and high/low. Players can choose any base-unit size they prefer, although smaller units are advisable.

Let’s see how the Martingale works with an example from roulette. Suppose you decide to use $10 as your base unit and bet on black. If black lands, you continue betting $10 until a loss occurs. When red appears and you lose your $10, you double the next wager to $20. If red appears again, you raise your next stake to $40. Should another loss occur, your following bet should be $80, and so on.

The idea is that you will eventually register a win that offsets your previous losses and leaves you with a profit equal to your base betting unit, which is $10 in this example. Regardless of how many losses you incur in a row or what base-unit size you use, you will finish the progression with a profit equal to the amount staked on the first spin if you can continue until you win.

The Martingale can yield positive results in the short term, but there is no way to know with certainty when a losing streak will end. Six or seven consecutive losing spins are entirely possible in roulette.

Because the bet size rises rapidly with the Martingale, a longer losing streak can either wipe out your bankroll or cause you to reach the table limits, preventing you from continuing the progression. Ultimately, you risk large amounts just to offset your losses and end up with only one base unit of profit.

The Fibonacci – How Nature's Code is Used at the Roulette Table

The Fibonacci sequence was first recorded by Italian mathematician Leonardo Pisano Bigollo, also known as Leonardo of Pisa or simply Fibonacci. In his 1202 book Liber Abaci, he described a sequence of numbers whose significance extends far beyond mathematics. Often called “Nature’s Code,” this sequence can be found throughout nature and even in the arts.

It runs as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, and so on. Each subsequent number equals the sum of the two numbers that precede it, a process that can continue indefinitely. So how is it used in roulette, and for what purpose?

In gambling, the Fibonacci is a negative progressive system in which the player increases their stake after each loss by following the famous sequence. After a win, the bettor moves two numbers back in the sequence. If the first wager wins, you continue flat betting your base unit until a loss occurs, which then calls for a bet increase.

The zero is ignored here, so the sequence becomes 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The system is mainly used for outside propositions in roulette and pass-line wagers in the dice game of craps. Here is how the Fibonacci is applied in practice when you start with a base unit of $10:

This system has a less steep betting progression than the Martingale, but it can still put large sums at risk if a prolonged losing streak occurs. The Fibonacci requires a sizable bankroll and a high tolerance for risk if the player intends to sustain the progression through a long losing streak.

Henry Labouchere's Contribution to Progressive Systems

The Labouchere system is commonly associated with avid gambler Henry Labouchere, who applied it specifically to roulette. Also known as the Cancellation Method or the Split Martingale, its original conception is sometimes attributed to the French mathematician and philosopher Marquis de Condorcet.

This is a negative progressive system that stands out for its higher level of complexity, so keep a pen and notepad handy if you decide to use it. Like other strategies, it is employed predominantly for even-money propositions in roulette. You begin by writing down a sequence of positive numbers. Choose the sequence carefully because your target profit equals the total of the numbers you list.

For example, take the sequence 1, 2, 3, 4, 5, with each number representing the units you will stake. In this case, your target profit is 15 units. We will use $1 as the base unit, but you can select any amount you find comfortable.

Your first wager should equal the sum of the first (1) and last (5) numbers in the sequence, which is $6 in this case. Each time you suffer a loss, you add the amount of the losing wager to the end of the sequence.

If you lose on the first round, your sequence becomes 1, 2, 3, 4, 5, 6, and your next bet is $7. Should you win this time, you end up with a net profit of one base unit, or $1.

Whenever your wager wins, you cross out the first and last numbers in the sequence. After winning the $7 wager, you cross out 1 and 6 and bet the sum of the first and last uncrossed numbers, or $7 (2+5). If you win again, you cross out 2 and 5, then stake 7 units (3+4), or another $7. A betting cycle ends successfully when you have crossed out all the numbers in your sequence.

Remember that the longer your sequence is, the more money you must bring to the roulette table. If you hit an extended losing streak, you will keep adding numbers to the sequence until you either exhaust your session bankroll or reach the table maximum.

Many roulette players who use the Labouchere decide in advance how many units they want to win and then select a sequence of numbers whose total equals that amount. For instance, if your goal is 20 units, you might use a sequence such as 1, 2, 3, 4, 5, 5.

On the Positive Side of Things – The Paroli

So far, we have covered only roulette systems that rely on negative betting progressions. The Paroli is different because it is based on a positive progression, meaning you increase your stakes when you win and reduce them after you lose. Accordingly, this approach focuses on maximizing profits rather than controlling losses.

The word “paroli” comes from the Latin “par,” which means “match.” The system is essentially the opposite of the Martingale, but it sets a limit on the player’s maximum bet. It is intended for even-money bets in games such as roulette, baccarat, craps, and blackjack.

You begin by choosing a fixed base-bet unit that is proportionate to your session bankroll. For instance, if you allocate $400 or $500 per session, your fixed unit should be no more than $10. Each time you win, you double your bet for the next round. If your first wager of $10 wins, you stake $20 on the next spin. If you win again, your following bet is $40.

The difference is that this doubling does not continue indefinitely. It stops once you score three consecutive wins, after which you return to your base unit. If a loss occurs at any point, you immediately revert to the base bet and continue flat betting that amount until you win.

The Paroli has several structural advantages over negative progressions in the short term. First, it prevents you from chasing your losses with progressively larger wagers during a bad run. Second, it aims to capitalize on short winning streaks. Third, it caps your maximum stake, reducing the amount of money you expose to risk.

D'Alembert and the Theory of Equilibrium

The D’Alembert system is named after the French mathematician, music theorist, and physicist Jean le Rond D’Alembert, who introduced a concept known as the Theory of Equilibrium. In his 1754 article “Croix ou Pile,” D’Alembert claimed that the probability of a coin toss producing heads increases with each consecutive tails outcome.

Sounds familiar, right? As brilliant as this French mathematician was, he nonetheless succumbed to the Gambler’s Fallacy. The probabilities of a fair coin are not affected by previous results, yet gamblers still devised an entire betting system based on D’Alembert’s mistaken notion.

The D’Alembert is a negative progressive system that relies on the idea of equilibrium. In other words, the player is expected to lose roughly the same number of even-money propositions as they win. Red, odd, and low outcomes are expected to appear about as often as black, even, and high outcomes during a betting session.

The system is straightforward and easy to use in roulette. You start with a stake of one base unit and increase your bet by one unit after each consecutive loss. Thus, if you begin with a base unit of $10 and lose, your next stake is $20. If you lose again, the following wager should be $30, and so on.

This continues until a win occurs, at which point the next wager is reduced by one base unit. If you win on your first spin, you continue flat betting the base unit until you lose, then increase the subsequent wager.

You can secure a profit with the D’Alembert provided that you win roughly the same number of bets as you lose. Because the winning bets are placed at higher stakes than the losing ones, this balance can potentially leave you ahead at the end of the session.

However, there is no guarantee that such equilibrium will occur during any given session in the short term. A prolonged losing streak can eat up your bankroll with the D’Alembert, despite its gentler negative progression.

Oscar's Grind – A Simple System

The Oscar’s Grind system first gained prominence after the publication of The Casino Gambler’s Guide by Allan Wilson. It is based on a positive betting progression in which you increase your stake by one base unit after each win but wager the same amount after a loss. Ideally, this produces a profit of one base unit at the end of each betting cycle. The guiding principle is that the player never risks more money than is necessary to recover previous losses and secure a profit of one unit. Here is how Oscar’s Grind works in practice:

In this example, the player recoups prior losses and finishes with a profit of exactly one unit. If they choose to continue playing, they should begin a new cycle at the first level with one base unit.