Graphic courtesy pbs.org
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: (Submitted by a visitor)
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.
Anti-martingale System: (Submitted by a visitor)
Positive progression.
Remarks: pre-decide 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.
* Negative progression betting systems: You increase the bet when you lose. Require more capital and usually employed to force a winning outcome following a losing streak. (Nerve-wracking, very painful when you lose. Avoid these systems if you can.)
Interesting related link
Roulette Probability analysis and the double-up betting strategy (use of the Martingale System).
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