Your initial bet is 1 unit, the second 3 units, the third 2 units and the fourth 6 units. Let's assume that each unit is €10 and the odds are 1:1  even money.
The first bet is €10. When winning, €10 is added to the €20 on the table making the second bet €30. When winning again on the second bet, there would be €60 on the table. Of this you take down €40 and the third bet is now €20. If the third bet wins, you will have €40 on the table to which you add €20 making a total of €60 for the fourth bet.
If the fourth bet wins, there would be a total of €120 on the table, all of which is net profit. Now all the bet is taken down and you start the system all over again at €10. Also, each time you lose, at any level, you start all over again at €10.
If you lose the first bet, your loss is €10. The second level loss is €20 (because you added another €10). At the third level, a loss will give you a net profit of €20 (because you have taken down €40). At the fourth level, a loss leaves you breaking even (because you put back €20 out of the €40 taken down).
The attraction of this system is that you risk €20 at a chance of making €120 net profit. This means you can lose six times at the worst level (second bet), and with one win (a set of four wins in a row) get your money back.
The Martingale system:
Negative progression system, the oldest known system.
(See also "The Ormond System" below)The Martingale system is a very old and extremely simple system. It is based on the probability of losing infinite times in a row and is usually applied to 'even money' bets.
You start with one bet. If you win, you start again with one bet. If you lose, you double your bet. Each time you lose, you double your last lost bet. Eventually you are bound to win. When you win you would recover all your lost bets plus one unit (or chip) profit against your initial wager.
Although infallible in theory, the Martingale system requires a large bankroll, has a very low return and is a very risky one because of the maximum bet limits imposed by the casinos. If you run out of money or reach the house limit, you can lose a lot with no chance to recover your losses.
The Ormond System:
Negative progression, a variation of the Martingale System.
Assumes you will win before you reach the house limit and can bankroll the losing run. Bet an initial amount (N). For each win, on the next bet N again. For each lose bet N*x+N where x is the number of losing bets. Thus if you finally win, you will recover all bet money, plus N for every loss. The progression would look like this on a €5 table. 5, 15, 35, 75, 155, 315, etc. As with all negative progressions, and this one even more so, it requires more capital and is employed to force a winning outcome following a losing streak.
Antimartingale System:
Positive progression.
Remarks: predecide a win, say 7 units
Bet on red. if win leave the two on red (or switch to black if you feel like it). If win again leave the four on another even chance. If win the third in a row skim the seven and restart with one. Every time you lose restart with one.
The Paroli system:
Positive progression system,
the opposite of the Martingale System.
This system is in a way the opposite of the Martingale system. You start with one bet and you increase your bet when you win rather than when you lose.
However, you will need to plan a betting procedure whereby you know how far you will let the bet build before you take it down to the initial starting bet and how much to raise after each win. This obviously depends on the type of game played and the odds of the bet.The advantage of this system is that you do not require a large bankroll. It lets the profit run and cuts short the losses.
The Parlay system:
Positive progression system, similar to the Paroli System.
This system is similar to the Paroli system and has the effect of 'pyramiding' your profit. Pyramiding is a parlay wager whereby the original wager plus its winnings are played on successive wagers.
It is commonly used in horse racing betting. Basically you make a bet and if you win you reinvest the winnings on the next bet. You 'let it ride'.
This method of play is by no means risk free, but it offers the least amount of risk of all wagers since the player is only concerned with either a win, place or show selection or a combination of the three.
It is one of the oldest methods of wagering and was originally derived from the same premise that banking systems use to compound interest.
The Labouchere system:
Negative progression system, also called the 'Cancellation System'.
(See also "The Labouchere System in Reverse" below)This system is also called the 'Cancellation' system. There are many variations. In its simplest form, you write down a series or a set of numbers; say, 1 2 3 4 5 6. The series can be short or long and not necessarily sequential such as 1 1 1 3 3 5 7. The choice of a particular series depends on the type of game you want to apply it to and the odds of the bet.
Each number represents the amount in units or chips to bet. You bet the first and last of these numbers. In this example 1 and 6, which totals 7 units.
If you win, you cross out the two numbers and bet the next two 'ends' (the outside numbers). In this instance 2 and 5. If you win again you bet on the next two remaining numbers 3 and 4, and if you win that too, you would have made a 'coup' or completed one game. Then you start all over again.
If you lose, then you add that one number to the end of the series. Say you lost your first bet of 7 units (1+ 6). Then you add number 7 to the end of the series to look like this: 1 2 3 4 5 6 7 and your next bet would be 8 units (1+ 7). If you won the first bet but lost the second 2 and 5, then the series of numbers would look like this: 2 3 4 5 7.
If you work it out, you will see that when the series is completed or when you make a 'coup', there is always a profit. The negative side of this system is that you could end up betting large sums of money even if your initial bet is small.
The Labouchere System in Reverse:
Add winnings to the sequence instead of losses. If you win, add one number (the winning units) to the end of the series. If you lose, delete two outside numbers. Put an appropriate target of, say, 20 units profit for 'even money' bets (less for higher odds), and when reached begin another sequence. Sequence commencement is 1,2,3,4 so you risk only 10 units per sequence.
The Labouchere System in Reverse is a positive progression betting system.
The Winner's Edge System  A variant of the Labouchere System in Reverse:
(Note: The description of the system is reproduced below the exact way it was submitted, word for word. The idea behind this system seems to make a lot of sense. However, the betting procedure and the amounts involved are not clear. If anyone can help in clarifying this, it will be greatly appreciated.)
"This is one invited by a Canadian many years ago. It is like the Cancellation System above with this variation: When winning, (add the first and last number in the sequence), the first time, and then 3 numbers until you lose. If you lose, add that to the end of the sequence and bet only the first (only one) number not crossed off. If you lose again, go to betting the unit bet, to preserve capital. I have found one needs about 40 times the first number in the sequence when starting as a bankroll , with the initial numbers being about 40202020 % (ie €50. sequence would be written: €20101010). Your bankroll taken to the table will be €1000.00.This means, I've found that you only have to win 30% of the time to be successful. I have used this very successfully in the casinos, to the point that I was asked to leave the table several times, as the casinos dont want consistent winners. It scares them. This system requires nerve, fearlessness and an appropriate bank roll. WHen playing Baccarrat, I was winning €4000. an hour , but again, don't back off pushing the money out, or you will lose. The system really forces one to bet large when winning and small when losing, which is exactly the opposite of what most people do and what the casino expects. You also need high enough table limits . It can be used playing blackjack, baccarrat or roulette, but is best for blackjack. Make sure you get their OK to write the bets down before you start, and tell them you are not counting cards."
The D'Alenbert system:
Negative progression and insurance system.
This is a mixture of Martingale and Insurance systems. Bets are raised one unit after each losing bet and lowered one unit after each winning bet. The sequence and amount raised or lowered can be varied to suit particular games and odds.
courtesy of www.ildado.com
