Anti-Martingale Roulette System

As the name of this Roulette system suggests, Anti-Martingale is an opposite strategy to its more famous colleague Martingale.

The Principle of the Anti-Martingale System

The principle of the Anti-Martingale system in Roulette again consists in doubling the bets. However not after each losing spin as in case of Martingale, but after a winning one. Therefore the Anti-Martingale system is a kind of the sequel bet. The win (and the risk) depends on the length of the sequel, which you can set in advance.

Even-money bets with the payout ratio 1:1 are used again (Low/High, Red/Black, Even/Odd numbers). For instance you can decide to bet on the red color five times in a row or you can bet alternately on red and black numbers, or even on any other combination of even-money bets (payout 1:1).

How to Use the Anti-Martingale Strategy

Make a bet of one unit ($1, $10, ...) on the first bet of your sequel. If you win, leave your win including your initial bet on the table (or move it to the place of the next bet in your sequel), so that you raise your initial bet by the achieved win. Keep betting in such way until you finish your sequel. It means that you bet 1, 2, 4, 8, 16, 32, 64, 128... units consequently.

Table 1: Winning chances of the Anti-Martingale Strategy in Roulette
Number of spinsProbability of winning the whole sequelProbability against winning the whole sequelPossible net win (in units)Possible loss (in units)Expected value (House edge)

Please note that the calculations in the table above apply to the French Roulette with a single zero only. The winning chance in American Roulette is lower due to the presence of the double zero. If you are interested in such calculations, follow clear exhibits on the page devoted to the expected value.

Comments on the Winning Chances of the Anti-martingale System

Let us say that you bet on the sequel of 5 spins. The probability to win the whole sequel is 2.72% only. This is because it deals with the consequent events, whereas the probabilities are multiplied. There are 18 winning possibilities out of the total 37 (there are 36 regular numbers plus zero in Roulette). The probability to win the whole sequel (5 spins in a row) is then (18/37)= 0.0272 = 2.72%). The probability of not finishing the whole sequel is the remainder: 100% – 2.72% = 97.28%.

If you managed to win the whole sequel, your net profit would be 31 units (i.e. $31 if you bet $1 at the start). How do we arrive at this figure? You bet 1 unit in the first round, if you win, your net profit is 2 × 1 – 1 (the initial bet) = 1 unit. In the second round you can bet 1 initial unit + 1 unit that you have just won. If you win again, the net profit is 2 × 2 – 1 = 3 etc. So this formula can be used generally: 25 – 1 = 32 – 1 = 31 units (the exponent is the length of the sequel).

As it was said, if you fail to complete the whole sequel, you will always lose one unit only. The expected value says what your return likely would be in a long period (or a great number of spins). The word "house edge" is the synonym as your (expected) loss is casino's (expected) gain.

Evaluation of the Anti-martingale System

Despite it is not easy to finish the whole sequel, especially a long one, the good thing about the Anti-Martingale system is that every time you lose (i.e. fail to complete the sequel), it costs you only the one initial unit (→ Roulette Record Series).

Testing Roulette Systems