Progressive Roulette Systems

Martingale - The King of Betting Progressions

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

This is a negative progressive system where you double your stake each time you lose and reduce it to your base unit after you score a win. It can be applied to all types of roulette bets but is mostly used for even-money propositions like red/black, even/odd, and high/low. The player can use any size of base unit they prefer although smaller units are recommendable.

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 hits, you continue betting $10 until a loss occurs. Red shows, you lose your $10 and double up to $20 on the next spin. If red comes again, you increase your next wager to $40. Should another loss occur, your next bet should be to the amount of $80 and so on.

The idea here is that you will eventually register a win which will offset your previous losses, leaving you with a profit equal to your base bet unit, $10 in this instance. Regardless of how many losses you have incurred in a row and what size of base unit you use, you will win exactly the amount you have staked on the first spin.

The Martingale can yield positive results in the short term but the trouble is there is no way for the player to know with certainty when the losing streak will break. Six or seven consecutive losing spins are not all that improbable in roulette.

The bet increase is rapid with the Martingale and a longer losing streak may either wipe out your entire bankroll or cause you to reach the table limits so that you are unable to continue with the progression. You ultimately risk large amounts just to offset your losses and end up with one base unit in profits.

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

The Fibonacci sequence was first put down on paper by Italian mathematician Leonardo Pisano Bigollo (also known as Leonardo of Pisa or Fibonacci). In his 1202 book Liber Abaci, he wrote about a sequence of numbers that goes way beyond the scope of mathematics. Often called “Nature’s Code”, this sequence can be found everywhere in nature and even in arts.

It runs in the following way – 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 510 etcetera. Each number to follow is equal to the sum of the two numbers that precede it, a process which can continue indefinitely. So how is this used in roulette and to what purpose?

In the context of gambling, the Fibonacci is a negative progressive system where the player increases their stake after each loss according to the famed sequence. When they register a win, they go two numbers back in the sequence. If the very first wager wins, you continue flat betting your base unit until a loss eventually occurs, calling for a bet increase.

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

It is obvious this system has a much steeper betting progression than the Martingale so that the player would inevitably expose huge amounts at risk should a long losing streak occur. This system is suitable for players who have large bankrolls to play with and are comfortable with the high level of risk involved.

Henry Labouchere's Contribution to Progressive Systems

The Labouchere system was discovered by keen gambler Henry Labouchere who applied it specifically to the game of roulette. It is also known as the Cancellation Method and Split Martingale. However, the original inventor of this system is said to be the French mathematician and philosopher Marquis de Condorcet.

This is a negative progressive system that stands out with a higher level of complexity so be sure to have a pen and a notepad nearby if you decide to use it. Like other strategies, this one is also used predominantly for even-money propositions in roulette. You start by writing down a sequence of positive numbers. Choose your sequence carefully since your potential profit is equal to the total of the numbers you pick.

Let’s use an example with the sequence 1, 2, 3, 4, 5, with each of these numbers corresponding to the number of units you need to stake. Your potential winnings should amount to 15 units in this case. We shall use $1 for our base unit but you can choose any amount you are comfortable with.

Your first wager should be equal to the total of the first (1) and the last (5) number in the sequence, in this case, $6. Each time you suffer a loss, you add the total of the losing wager at the end of the sequence.

Thus, if you lose on the very first round of play, your sequence would look like this: 1, 2, 3, 4, 5, 6 and your next bet would be $7. Provided that you win this time, you end up with a net profit of 1 base unit, or $1.

Every time your wager wins, you cross out the first and the last number in the sequence like so 1, 2, 3, 4, 5, 6 and bet the total of the first and last uncrossed numbers, or $7 (2+5). You win again and your sequence becomes 1, 2, 3, 4, 5, 6. Therefore, you bet 7 units (3+4) or another $7. A betting cycle ends successfully when you cross out all numbers in your sequence.

Keep in mind that the longer your sequence is, the more money you need to bring with you to the roulette table. If you hit a longer losing streak, you will keep adding numbers to the sequence until you either lose your entire session bankroll or reach the table maximum.

Many roulette players who resort to the Labouchere determine how much they want to win (in units) beforehand and pick a sequence of numbers whose total adds up to that amount. For example, if your win goal is 20 units, you use a sequence like 1, 2, 3, 4, 5, 5.

On the Positive Side of Things – The Paroli

So far we have discussed only roulette systems that rely on negative betting progressions. The Paroli is different because it is based on a positive progression where you increase the stakes when you win and reduce them after you lose. Respectively, this system aims at profit maximization instead of loss control and reduction.

The root of the word “paroli” comes from the Latin “par”, which means “match”. This system is practically the opposite of the infamous Martingale but it sets limits on the player’s maximum bet. It is intended for even-money bets in games like roulette, baccarat, craps, and blackjack.

You again start by deciding on a fixed base bet unit, which should be proportionate to your session’s bankroll. For example, 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. So if your first bet is to the amount of $10 and you win, you stake $20 on the next spin. Win again and your next bet is $40.

The difference here is that this doubling does not go on indefinitely. It stops as soon as you score three wins in a row, after which you reduce your next wager to your chosen base unit. Should a loss occur, you drop down to the base bet unit and continue to flat bet this amount until you win.

The Paroli has several advantages in the short term. First, it prevents you from chasing your losses by dramatically increasing your wagers during a bad run. Second, it helps you generate small but consistent short-term profits. And third, it sets a limit on your maximum stake which prevents you from exposing too much money 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 eu Pile, D’Alembert claimed that the probability of a coin toss producing heads increases with each consecutive outcome of tails that occurs.

Sounds familiar, right? As brilliant as this French mathematician was, he, too, succumbed to the Gambler’s Fallacy. The probabilities of a fair coin are not affected by previous results, which did not prevent gamblers from devising an entire betting system based on D’Alembert’s false notion.

The D’Alembert is a negative progressive system that relies on the notion of equilibrium, i.e. the player would lose approximately the same number of even-money propositions as they would win. In other words, the idea here is that red, odd, and low outcomes will occur roughly the same number of times as black, even, and high outcomes during a betting session.

The system is quite straightforward and easy to use in roulette. You start the session with a stake equal to one base unit and increase your bet with one unit after each consecutive loss. Thus, if you start the session with a base unit of $10 and lose, your next stake would be $20. If another loss occurs on the next round, your next bet should be equal to $30 and so on.

This continues until a win occurs, in which case the next wager is reduced by one base unit. If you win with your very first wager at the start of the session, you continue flat betting the base unit until you lose and increase the next wager.

You can register some profits with the D’Alembert provided that you win approximately the same number of bets as those you lose. The winning bets are made at higher stakes than the losing ones, which potentially enables you to end the session on profit.

However, there is no guarantee this equilibrium between winning and losing wagers will occur during any given session in the short-term. A longer losing streak can eat up your bankroll with the D’Alembert despite its less steep 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 book by Allan Wilson. It is based on a positive betting progression where you increase your stakes by one base unit after each win but stake the same amount when you lose. This should result in a win of one base unit at the end of each betting cycle. The idea here is that the player never exposes more money to risk than the amount they need to recover their previous losses and turn up a profit of one base unit. Here is how the Oscar’s Grind applies in practice:

Here the player has succeeded in recouping their prior losses and has ended up with profits of exactly one unit. If they decide to continue playing, they need to start another cycle at the first level with one base unit.