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Understanding the D’Alembert system and its use in roulette


1 Mar 2018

For a bet considered to have a 50/50 chance of winning, it must have only two outcomes which are equally likely of occurring. Calling heads or tails on a fair coin would fit this criteria.

Head over to the roulette wheels within a casino and three bets are typically plugged as being 50/50 outcomes – red or black, odd or even and the two betting sections incorporating the numbers 1-18 and 19-36.

However, all of these bets would be losers should the spinning roulette ball come to rest in any green section of the wheel. Play European roulette and there is a single green 0, while American roulette also has a green 00.

These ensure that the so-called 50/50 bets do not have a 50% likelihood of occurring. Bet red on a European wheel and the probability of a win is 48.6%, while this drops to 47.4% on an American wheel.

Martingale system

Within the gambling landscape, there are a considerable number of betting systems that brandish the promise of a guaranteed profit if followed.

One of the more recognised is the Martingale strategy, which at its core is incredibly simple to follow and focuses on these alleged 50/50 bets. A player must decide on their bet of choice and their initial stake, such as opting for black and £10.

If the bet wins, they place it identically again. If it loses, they double their stake. The stake continues to double after every loss, until eventually a win occurs. At this point, the stake returns to its initial level.

The feeling is that should a player lose £10, then £20, then £40 and £80, one winning £160 bet would not only cancel out the previous run of losses, but also provide a small profit on top.

The main drawbacks of this system are that a lengthy losing sequence could very quickly wipe a person’s bankroll and that it wouldn’t take long for the size of the stake to surpass any roulette table maximums.

D’Alembert system

There are some clear similarities between the D’Alembert and Martingale systems. Top of these characteristics is that a player scales their bet based on the performance of the previous one.

Where the two systems differ is in the betting progression. A player is not expected to double their stake after a losing bet, just up it by a single unit. So, a losing £10 bet, becomes £20 and then £30, rather than £10 becoming £20 and then £40.

This scaling also takes place once a winning bet has been registered. Rather than immediately returning to the initial stake, a player reduces their bet size in the same way it was increased after a loss.

Using the example above, the next bet after a win at £30 using the Martingale strategy would be £10. Adopting the D’Alembert strategy would mean staking £20 for the next spin.


The D’Alembert system is one of the more straightforward to implement, following simple calculations to either increase or decrease bet size.

Particularly compared to the Martingale, it also allows a player to stay in better control of their bankroll.

If playing on a European wheel with just the single zero, the probability of five reds, blacks, odds or evens being spun in succession is 2.72%. It is not unreasonable for a player to have to negotiate such a losing streak in every roulette session.

Using Martingale and starting by betting £10, they would be down £310 at this stage and faced with staking a further £320 on the next spin. With D’Alembert, their losses would be £150 and their next bet would be £60.

It does a far better job at keeping losses to a minimum and making a bankroll survive for longer, especially in those more troublesome moments when losses can start to mount up.


On the flip side of this, one single win using D’Alembert fails to wipe away a run of losses like it does in Martingale.

Using the same losing streak as above, a winning £320 Martingale bet, would not only repay the £310 previously lost, but also provide £10 profit for the session.

A win on the £60 D’Alembert bet would only return a profit of the same amount, even though £150 had been lost in the previous spins. This means the player is still down £90.

Therefore, although a player should have the balance to withstand a run of losses, they are likely to struggle to recoup it all.

Reverse Reverse

Players also have the option of adopting a reverse D’Alembert strategy, where they increase their wager after winning a hand and decrease it after a loss.

This could prove highly favourable during a winning sequence, but leave players at a loss during an even betting sequence.

Imagine a sequence of win, loss, win, loss, win and loss. With the standard D’Alembert strategy starting at £10, a player would win £10, lose £10, win £20, lose £10, win £20 and lose £10. Thus, making a profit of £20.

With the reverse they would win £10, lose £20, win £10, lose £20, win £10 and lose £20. So, despite three winning spins and three losing ones, a player would be down £30.